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<a NAME="E1:113"/><i><font color="Green" title="E96">A1</font></i>: 
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_1"><b>proof </b></a><div class="add">

<a NAME="E1:113_1"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
;<br/>
<b>hence </b><a NAME="E2:113_1"/>
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:113"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="113_2"><b>proof </b></a><div class="add">

<a NAME="E1:113_2"/>
<span class="p1">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 0
 
;<br/>
<b>hence </b><a NAME="E2:113_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 256</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 <b>by </b><i><a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:113"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">64 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 128</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 0
 
<b>by </b><i><a class="txt" href="pepin.html#E1:113"><i><font color="Green" title="E96">A1</font></i></a>, <a class="txt" href="pepin.html#E117"><i><font color="Green" title="E93">Lm51</font></i></a>, <a class="ref" href="euler_2.html#T8" title="EULER_2:th.8">EULER_2:8</a></i>;<br/>
<a NAME="E4:113"/><b>then </b>
 <a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">64 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p4">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 128</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span>
 
<b>by </b><i><a class="ref" href="nat_d.html#T6" title="NAT_D:th.6">NAT_D:6</a></i>;<br/>
<b>hence </b><a NAME="E5:113"/>
 <a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default">3 <a href="newton.html#K16" title="NEWTON:func.16">|^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">64 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 0</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p3">(<span class="default">256 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 128</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="pepin.html#T7" target="_self" title="PEPIN:th.7">Th7</a></i>;<br/>


</div>
