<?xml version="1.0"?>
<div class="add">

<a NAME="E1:45"/><i><font color="Green" title="E44">A1</font></i>: 
2503 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 139 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 18
 
;<br/>
<a NAME="E2:45"/><i><font color="Green" title="E45">A2</font></i>: 
139 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 139 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>;<br/>
<i><font color="Green" title="E46">A3</font></i>: 139 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 18 = 
<span class="p1">(<span class="default">13 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p2">(<span class="default">18 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 7</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 18

<br/>.= 
13 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">13 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 5</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 5</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 5
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
3 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p2">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default">1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 2
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
1 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 2
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T64" title="NEWTON:th.64">NEWTON:64</a></i>
;<br/>
<a NAME="E4:45"/>
2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="newton.html#T10" title="NEWTON:th.10">NEWTON:10</a></i>;<br/>
<a NAME="E5:45"/><b>then </b><i><font color="Green" title="E47">A4</font></i>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>;<br/>
<i><font color="Green" title="E48">A5</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
<span class="p1">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E5:45"><i><font color="Green" title="E47">A4</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
<br/>.= 
4
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>
<i><font color="Green" title="E49">A6</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
<span class="p1">(<span class="default">4 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E6:45"><i><font color="Green" title="E48">A5</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
<br/>.= 
16
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>
<i><font color="Green" title="E50">A7</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 8</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
<span class="p1">(<span class="default">16 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 16</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E7:45"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
<br/>.= 
256
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>
<a NAME="E9:45"/>
256 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 256 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 26</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 458
 
;<br/>
<a NAME="E10:45"/><b>then </b><i><font color="Green" title="E51">A8</font></i>: 
<span class="p1">(<span class="default">256 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 256</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 458
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E52">A9</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 16</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 8</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
458
<b>by </b><i><a class="txt" href="#E8:45"><i><font color="Green" title="E50">A7</font></i></a>, <a class="txt" href="#E10:45"><i><font color="Green" title="E51">A8</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E12:45"/>
458 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 458 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 83</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2015
 
;<br/>
<a NAME="E13:45"/><b>then </b><i><font color="Green" title="E53">A10</font></i>: 
<span class="p1">(<span class="default">458 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 458</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2015
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E54">A11</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 32</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 16</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
2015
<b>by </b><i><a class="txt" href="#E11:45"><i><font color="Green" title="E52">A9</font></i></a>, <a class="txt" href="#E13:45"><i><font color="Green" title="E53">A10</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E15:45"/>
2015 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2015 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1622</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 359
 
;<br/>
<a NAME="E16:45"/><b>then </b><i><font color="Green" title="E55">A12</font></i>: 
<span class="p1">(<span class="default">2015 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2015</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 359
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E56">A13</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 64</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 32</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
359
<b>by </b><i><a class="txt" href="#E14:45"><i><font color="Green" title="E54">A11</font></i></a>, <a class="txt" href="#E16:45"><i><font color="Green" title="E55">A12</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E18:45"/>
359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 359 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 51</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1228
 
;<br/>
<a NAME="E19:45"/><b>then </b><i><font color="Green" title="E57">A14</font></i>: 
<span class="p1">(<span class="default">359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 359</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1228
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E58">A15</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 128</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 64</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
1228
<b>by </b><i><a class="txt" href="#E17:45"><i><font color="Green" title="E56">A13</font></i></a>, <a class="txt" href="#E19:45"><i><font color="Green" title="E57">A14</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E21:45"/>
1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1228 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 602</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1178
 
;<br/>
<a NAME="E22:45"/><b>then </b><i><font color="Green" title="E59">A16</font></i>: 
<span class="p1">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1228</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1178
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E60">A17</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 256</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 128</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
1178
<b>by </b><i><a class="txt" href="#E20:45"><i><font color="Green" title="E58">A15</font></i></a>, <a class="txt" href="#E22:45"><i><font color="Green" title="E59">A16</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E24:45"/>
1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1178 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 554</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1022
 
;<br/>
<a NAME="E25:45"/><b>then </b><i><font color="Green" title="E61">A18</font></i>: 
<span class="p1">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1178</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1022
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E62">A19</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 512</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 256</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
1022
<b>by </b><i><a class="txt" href="#E23:45"><i><font color="Green" title="E60">A17</font></i></a>, <a class="txt" href="#E25:45"><i><font color="Green" title="E61">A18</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E27:45"/>
1022 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1022 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 417</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 733
 
;<br/>
<a NAME="E28:45"/><b>then </b><i><font color="Green" title="E63">A20</font></i>: 
<span class="p1">(<span class="default">1022 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1022</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 733
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E64">A21</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 1024</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 512</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
733
<b>by </b><i><a class="txt" href="#E26:45"><i><font color="Green" title="E62">A19</font></i></a>, <a class="txt" href="#E28:45"><i><font color="Green" title="E63">A20</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E30:45"/>
733 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 733 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 214</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1647
 
;<br/>
<a NAME="E31:45"/><b>then </b><i><font color="Green" title="E65">A22</font></i>: 
<span class="p1">(<span class="default">733 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 733</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1647
 
<b>by </b><i><a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>
<i><font color="Green" title="E66">A23</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2048</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1024</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
1647
<b>by </b><i><a class="txt" href="#E29:45"><i><font color="Green" title="E64">A21</font></i></a>, <a class="txt" href="#E31:45"><i><font color="Green" title="E65">A22</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self" title="NAT_4:th.11">Th11</a></i>
;<br/>
<a NAME="E33:45"/><i><font color="Green" title="E67">A24</font></i>: 
359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 64 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 9</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 449
 
;<br/>
<a NAME="E34:45"/><i><font color="Green" title="E68">A25</font></i>: 
1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 449 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 220</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 712
 
;<br/>
<a NAME="E35:45"/><i><font color="Green" title="E69">A26</font></i>: 
1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 712 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 335</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 231
 
;<br/>
<a NAME="E36:45"/><i><font color="Green" title="E70">A27</font></i>: 
1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 231 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 152</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
;<br/>
<i><font color="Green" title="E71">A28</font></i>: 2503 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 = 
2503 <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1
<b>by </b><i><a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>
<br/>.= 
2502

;<br/>
<b>then </b><i><font color="Green" title="E72">A29</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2503 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">2048 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 454</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2048</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 454</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2048</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p4">(<span class="default">256 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 198</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 256</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 198</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E32:45"><i><font color="Green" title="E66">A23</font></i></a>, <a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p0">(<span class="default">128 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 70</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E23:45"><i><font color="Green" title="E60">A17</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 128</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 70</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 6</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E20:45"><i><font color="Green" title="E58">A15</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 64</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 6</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p4">(<span class="default">4 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E17:45"><i><font color="Green" title="E56">A13</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 4</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">16 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E6:45"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="#E7:45"><i><font color="Green" title="E49">A6</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">359 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 64</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1228 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 449</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E33:45"><i><font color="Green" title="E67">A24</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">1178 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 712</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E34:45"><i><font color="Green" title="E68">A25</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">1647 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 231</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E35:45"><i><font color="Green" title="E69">A26</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="#E36:45"><i><font color="Green" title="E70">A27</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
;<br/>
<a NAME="E39:45"/><i><font color="Green" title="E73">A30</font></i>: 
2502 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">139 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 18</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E40:45"/><i><font color="Green" title="E74">A31</font></i>: 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="binop_2.html#K10" title="BINOP_2:func.10">-</a> 1
 
<b>by </b><i><a class="ref" href="prepower.html#T19" title="PREPOWER:th.19">PREPOWER:19</a>, <a class="ref" href="xreal_1.html#T235" title="XREAL_1:th.235">XREAL_1:235</a></i>;<br/>
<i><font color="Green" title="E75">A32</font></i>: <span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503 = 
<span class="p1">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default">16 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 16</span>)</span> <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> <span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">458 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 4</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503
<b>by </b><i><a class="txt" href="#E6:45"><i><font color="Green" title="E48">A5</font></i></a>, <a class="txt" href="#E11:45"><i><font color="Green" title="E52">A9</font></i></a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></i>
<br/>.= 
1832
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
;<br/>
<a NAME="E42:45"/><i><font color="Green" title="E76">A33</font></i>: 
4334 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1831
 
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2503 <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 139</span>)</span></span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 2503 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 2503
<b>by </b><i><a class="txt" href="#E37:45"><i><font color="Green" title="E71">A28</font></i></a>, <a class="txt" href="#E39:45"><i><font color="Green" title="E73">A30</font></i></a>, <a class="ref" href="nat_d.html#D1" title="NAT_D:def.1">NAT_D:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p2">(<span class="default">2503 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span></span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 2503
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
2503 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 18</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2502</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span>
<b>by </b><i><a class="txt" href="#E40:45"><i><font color="Green" title="E74">A31</font></i></a>, <a class="ref" href="nat_d.html#T28" title="NAT_D:th.28">NAT_D:28</a></i>
<br/>.= 
2503 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1832 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <span class="p3">(<span class="default">2502 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span>
<b>by </b><i><a class="txt" href="#E41:45"><i><font color="Green" title="E75">A32</font></i></a>, <a class="ref" href="euler_2.html#T8" title="EULER_2:th.8">EULER_2:8</a></i>
<br/>.= 
2503 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1832 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2502</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2503</span>)</span>
<b>by </b><i><a class="ref" href="nat_d.html#T24" title="NAT_D:th.24">NAT_D:24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1831 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 672</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 1831
<b>by </b><i><a class="txt" href="#E42:45"><i><font color="Green" title="E76">A33</font></i></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>
<br/>.= 
672 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">672 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 487</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">487 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 185</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 487
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
185 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">185 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 117</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">117 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 68</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 117
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
68 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">68 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 49</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">49 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 19</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 49
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
19 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">19 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 11</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">11 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 8</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 11
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
8 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">8 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 2</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 2</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 3
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
2 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24" title="BINOP_2:func.24">*</a> 1</span>)</span> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
2 <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> 1
<b>by </b><i><a class="ref" href="euler_1.html#T9" title="EULER_1:th.9">EULER_1:9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T64" title="NEWTON:th.64">NEWTON:64</a></i>
;<br/>
<b>hence </b><a NAME="E44:45"/>
2503 is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>
 <b>by </b><i><a class="txt" href="#E1:45"><i><font color="Green" title="E44">A1</font></i></a>, <a class="txt" href="#E2:45"><i><font color="Green" title="E45">A2</font></i></a>, <a class="txt" href="#E3:45"><i><font color="Green" title="E46">A3</font></i></a>, <a class="txt" href="#E38:45"><i><font color="Green" title="E72">A29</font></i></a>, <a class="ref" href="nat_4.html#T25" target="_self" title="NAT_4:th.25">Th25</a>, <a class="ref" href="nat_4.html#T34" target="_self" title="NAT_4:th.34">Th34</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
