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

<a NAME="E1:44"/><i><font color="Green">E43</font></i>: 
1259 <a href="binop_2.html#K10">-</a> 1 <a href="hidden.html#R1">=</a> 37 <a href="binop_2.html#K24">*</a> 34
 
;<br/>
<a NAME="E2:44"/><i><font color="Green">E44</font></i>: 
37 <a href="hidden.html#R1">=</a> 37 <a href="wsierp_1.html#K2">|^</a> 1
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<i><font color="Green">E45</font></i>: 37 <a href="nat_1.html#K8">hcf</a> 34 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">34 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="nat_1.html#K8">hcf</a> 34

<br/>.= 
3 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> 11</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
3 <a href="nat_1.html#K8">hcf</a> 1
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T64">NEWTON:64</a></i>
;<br/>
<a NAME="E4:44"/>
2 <a href="wsierp_1.html#K2">|^</a> 1 <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<a NAME="E5:44"/><b>then </b><i><font color="Green">E46</font></i>: 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>;<br/>
<i><font color="Green">E47</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 2</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
<span class="p1">(<span class="default">2 <a href="binop_2.html#K24">*</a> 2</span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E5:44"><i><font color="Green">E46</font></i></a></i>
<br/>.= 
4
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>
<i><font color="Green">E48</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 4</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
<span class="p1">(<span class="default">4 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E6:44"><i><font color="Green">E47</font></i></a></i>
<br/>.= 
16
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>
<i><font color="Green">E49</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 8</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
<span class="p1">(<span class="default">16 <a href="binop_2.html#K24">*</a> 16</span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E7:44"><i><font color="Green">E48</font></i></a></i>
<br/>.= 
256
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
;<br/>
<a NAME="E9:44"/>
256 <a href="binop_2.html#K24">*</a> 256 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 52</span>)</span> <a href="binop_2.html#K23">+</a> 68
 
;<br/>
<a NAME="E10:44"/><b>then </b><i><font color="Green">E50</font></i>: 
<span class="p1">(<span class="default">256 <a href="binop_2.html#K24">*</a> 256</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 68
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E51</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 16</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 8</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
68
<b>by </b><i><a class="txt" href="nat_4.html#E8:44"><i><font color="Green">E49</font></i></a>, <a class="txt" href="nat_4.html#E10:44"><i><font color="Green">E50</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self">Th11</a></i>
;<br/>
<a NAME="E12:44"/>
68 <a href="binop_2.html#K24">*</a> 68 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 3</span>)</span> <a href="binop_2.html#K23">+</a> 847
 
;<br/>
<a NAME="E13:44"/><b>then </b><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default">68 <a href="binop_2.html#K24">*</a> 68</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 847
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E53</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 32</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 16</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
847
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E11:44"><i><font color="Green">E51</font></i></a>, <a class="txt" href="nat_4.html#E13:44"><i><font color="Green">E52</font></i></a></i>
;<br/>
<a NAME="E15:44"/>
847 <a href="binop_2.html#K24">*</a> 847 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 569</span>)</span> <a href="binop_2.html#K23">+</a> 1038
 
;<br/>
<a NAME="E16:44"/><b>then </b><i><font color="Green">E54</font></i>: 
<span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> 847</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 1038
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E55</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 64</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 32</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
1038
<b>by </b><i><a class="txt" href="nat_4.html#E14:44"><i><font color="Green">E53</font></i></a>, <a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E16:44"><i><font color="Green">E54</font></i></a></i>
;<br/>
<a NAME="E18:44"/>
1038 <a href="binop_2.html#K24">*</a> 1038 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 855</span>)</span> <a href="binop_2.html#K23">+</a> 999
 
;<br/>
<a NAME="E19:44"/><b>then </b><i><font color="Green">E56</font></i>: 
<span class="p1">(<span class="default">1038 <a href="binop_2.html#K24">*</a> 1038</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 999
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E57</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 128</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 64</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
999
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E17:44"><i><font color="Green">E55</font></i></a>, <a class="txt" href="nat_4.html#E19:44"><i><font color="Green">E56</font></i></a></i>
;<br/>
<a NAME="E21:44"/>
999 <a href="binop_2.html#K24">*</a> 999 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 792</span>)</span> <a href="binop_2.html#K23">+</a> 873
 
;<br/>
<a NAME="E22:44"/><b>then </b><i><font color="Green">E58</font></i>: 
<span class="p1">(<span class="default">999 <a href="binop_2.html#K24">*</a> 999</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 873
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E59</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 256</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 128</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
873
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E20:44"><i><font color="Green">E57</font></i></a>, <a class="txt" href="nat_4.html#E22:44"><i><font color="Green">E58</font></i></a></i>
;<br/>
<a NAME="E24:44"/>
873 <a href="binop_2.html#K24">*</a> 873 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 605</span>)</span> <a href="binop_2.html#K23">+</a> 434
 
;<br/>
<a NAME="E25:44"/><b>then </b><i><font color="Green">E60</font></i>: 
<span class="p1">(<span class="default">873 <a href="binop_2.html#K24">*</a> 873</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 434
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E61</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 512</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 256</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
434
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E23:44"><i><font color="Green">E59</font></i></a>, <a class="txt" href="nat_4.html#E25:44"><i><font color="Green">E60</font></i></a></i>
;<br/>
<a NAME="E27:44"/>
434 <a href="binop_2.html#K24">*</a> 434 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 149</span>)</span> <a href="binop_2.html#K23">+</a> 765
 
;<br/>
<a NAME="E28:44"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default">434 <a href="binop_2.html#K24">*</a> 434</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 <a href="hidden.html#R1">=</a> 765
 
<b>by </b><i><a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>
<i><font color="Green">E63</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 1024</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 512</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
765
<b>by </b><i><a class="ref" href="nat_4.html#T11" target="_self">Th11</a>, <a class="txt" href="nat_4.html#E26:44"><i><font color="Green">E61</font></i></a>, <a class="txt" href="nat_4.html#E28:44"><i><font color="Green">E62</font></i></a></i>
;<br/>
<a NAME="E30:44"/><i><font color="Green">E64</font></i>: 
847 <a href="binop_2.html#K24">*</a> 1024 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 688</span>)</span> <a href="binop_2.html#K23">+</a> 1136
 
;<br/>
<a NAME="E31:44"/><i><font color="Green">E65</font></i>: 
1038 <a href="binop_2.html#K24">*</a> 1136 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 936</span>)</span> <a href="binop_2.html#K23">+</a> 744
 
;<br/>
<a NAME="E32:44"/><i><font color="Green">E66</font></i>: 
999 <a href="binop_2.html#K24">*</a> 744 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 590</span>)</span> <a href="binop_2.html#K23">+</a> 446
 
;<br/>
<a NAME="E33:44"/><i><font color="Green">E67</font></i>: 
765 <a href="binop_2.html#K24">*</a> 446 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 271</span>)</span> <a href="binop_2.html#K23">+</a> 1
 
;<br/>
<i><font color="Green">E68</font></i>: 1259 <a href="binarith.html#K5">-'</a> 1 = 
1259 <a href="binop_2.html#K10">-</a> 1
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>
<br/>.= 
1258

;<br/>
<i><font color="Green">E69</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">1259 <a href="binarith.html#K5">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">1024 <a href="binop_2.html#K23">+</a> 234</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E34:44"><i><font color="Green">E68</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 1024</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 234</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="newton.html#T13">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="wsierp_1.html#K2">|^</a> 1024</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p4">(<span class="default">128 <a href="binop_2.html#K23">+</a> 106</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 128</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 106</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E29:44"><i><font color="Green">E63</font></i></a>, <a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p0">(<span class="default">64 <a href="binop_2.html#K23">+</a> 42</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E20:44"><i><font color="Green">E57</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 64</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 42</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">32 <a href="binop_2.html#K23">+</a> 10</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E17:44"><i><font color="Green">E55</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 32</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 10</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p4">(<span class="default">8 <a href="binop_2.html#K23">+</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E14:44"><i><font color="Green">E53</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 8</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E6:44"><i><font color="Green">E47</font></i></a>, <a class="txt" href="nat_4.html#E8:44"><i><font color="Green">E49</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> 1024</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">1038 <a href="binop_2.html#K24">*</a> 1136</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E30:44"><i><font color="Green">E64</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">999 <a href="binop_2.html#K24">*</a> 744</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E31:44"><i><font color="Green">E65</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">765 <a href="binop_2.html#K24">*</a> 446</span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E32:44"><i><font color="Green">E66</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
<br/>.= 
1
<b>by </b><i><a class="txt" href="nat_4.html#E33:44"><i><font color="Green">E67</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
;<br/>
<a NAME="E36:44"/><i><font color="Green">E70</font></i>: 
1258 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">37 <a href="binop_2.html#K24">*</a> 34</span>)</span> <a href="binop_2.html#K23">+</a> 0
 
;<br/>
<a NAME="E37:44"/>
2 <a href="wsierp_1.html#K2">|^</a> 34 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1
 
<b>by </b><i><a class="ref" href="prepower.html#T19">PREPOWER:19</a></i>;<br/>
<a NAME="E38:44"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="binarith.html#K5">-'</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="binop_2.html#K10">-</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#T50">BINARITH:50</a></i>;<br/>
<a NAME="E39:44"/><i><font color="Green">E72</font></i>: 
847 <a href="binop_2.html#K24">*</a> 4 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 2</span>)</span> <a href="binop_2.html#K23">+</a> 870
 
;<br/>
<i><font color="Green">E73</font></i>: <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="nat_1.html#K4">mod</a> 1259 = 
<span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">32 <a href="binop_2.html#K23">+</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 32</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
<span class="p1">(<span class="default">847 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="nat_1.html#K4">mod</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E14:44"><i><font color="Green">E53</font></i></a>, <a class="txt" href="nat_4.html#E6:44"><i><font color="Green">E47</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
870
<b>by </b><i><a class="txt" href="nat_4.html#E39:44"><i><font color="Green">E72</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
;<br/>
<a NAME="E41:44"/><i><font color="Green">E74</font></i>: 
2128 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 869
 
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">1259 <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K3">div</a> 37</span>)</span></span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K8">hcf</a> 1259 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="nat_1.html#K8">hcf</a> 1259
<b>by </b><i><a class="txt" href="nat_4.html#E34:44"><i><font color="Green">E68</font></i></a>, <a class="txt" href="nat_4.html#E36:44"><i><font color="Green">E70</font></i></a>, <a class="ref" href="nat_1.html#D1">NAT_1: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="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="binarith.html#K5">-'</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">1259 <a href="binop_2.html#K24">*</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K8">hcf</a> 1259
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
1259 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> 34</span>)</span> <a href="binop_2.html#K23">+</a> 1258</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E38:44"><i><font color="Green">E71</font></i></a>, <a class="ref" href="scmp_gcd.html#T1">SCMP_GCD:1</a></i>
<br/>.= 
1259 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">870 <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default">1258 <a href="nat_1.html#K4">mod</a> 1259</span>)</span></span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span>
<b>by </b><i><a class="txt" href="nat_4.html#E40:44"><i><font color="Green">E73</font></i></a>, <a class="ref" href="euler_2.html#T8">EULER_2:8</a></i>
<br/>.= 
1259 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">870 <a href="binop_2.html#K23">+</a> 1258</span>)</span> <a href="nat_1.html#K4">mod</a> 1259</span>)</span>
<b>by </b><i><a class="ref" href="nat_1.html#T76">NAT_1:76</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">869 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 390</span>)</span> <a href="nat_1.html#K8">hcf</a> 869
<b>by </b><i><a class="txt" href="nat_4.html#E41:44"><i><font color="Green">E74</font></i></a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
<br/>.= 
390 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">390 <a href="binop_2.html#K24">*</a> 2</span>)</span> <a href="binop_2.html#K23">+</a> 89</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">89 <a href="binop_2.html#K24">*</a> 4</span>)</span> <a href="binop_2.html#K23">+</a> 34</span>)</span> <a href="nat_1.html#K8">hcf</a> 89
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
34 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">34 <a href="binop_2.html#K24">*</a> 2</span>)</span> <a href="binop_2.html#K23">+</a> 21</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">21 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 13</span>)</span> <a href="nat_1.html#K8">hcf</a> 21
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
13 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">13 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 8</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">8 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 5</span>)</span> <a href="nat_1.html#K8">hcf</a> 8
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
5 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">5 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">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">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span> <a href="nat_1.html#K8">hcf</a> 3
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
2 <a href="nat_1.html#K8">hcf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 1</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
2 <a href="nat_1.html#K8">hcf</a> 1
<b>by </b><i><a class="ref" href="euler_1.html#T9">EULER_1:9</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="newton.html#T64">NEWTON:64</a></i>
;<br/>
<b>hence </b><a NAME="E43:44"/>
1259 is <a href="int_2.html#V1">prime</a>
 <b>by </b><i><a class="txt" href="nat_4.html#E1:44"><i><font color="Green">E43</font></i></a>, <a class="txt" href="nat_4.html#E2:44"><i><font color="Green">E44</font></i></a>, <a class="txt" href="nat_4.html#E3:44"><i><font color="Green">E45</font></i></a>, <a class="ref" href="nat_4.html#T31" target="_self">Th31</a>, <a class="txt" href="nat_4.html#E35:44"><i><font color="Green">E69</font></i></a>, <a class="ref" href="nat_4.html#T25" target="_self">Th25</a></i>;<br/>


</div>
