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

<a NAME="E1:113"/><i><font color="Green">E98</font></i>: 
1 <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span> <a href="hidden.html#R1">=</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">=</a> <span class="p1">(<span class="default">257 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
;<br/>
<b>hence </b><a NAME="E2:113_1"/>
1 <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 1
 <b>by </b><i><a class="ref" href="pepin.html#T58" target="_self">Th58</a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:113"/><i><font color="Green">E99</font></i>: 
257 <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span> <a href="hidden.html#R1">=</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"/>
257 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">257 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 0
 
;<br/>
<b>hence </b><a NAME="E2:113_2"/>
257 <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="pepin.html#T58" target="_self">Th58</a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">32 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 128</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span> = 
<span class="p1">(<span class="default">256 <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="pepin.html#E1:113"><i><font color="Green">E98</font></i></a>, <a class="txt" href="pepin.html#E103"><i><font color="Green">Lemma80</font></i></a>, <a class="ref" href="euler_2.html#T8">EULER_2:8</a></i>
<br/>.= 
0
<b>by </b><i><a class="txt" href="pepin.html#E2:113"><i><font color="Green">E99</font></i></a></i>
;<br/>
<a NAME="E4:113"/><b>then </b>
 <a href="pepin.html#K5" target="_self">Fermat</a> 3 <a href="nat_1.html#R1">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">32 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 128</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 3</span>)</span>
 
<b>by </b><i><a class="ref" href="nat_1.html#T53">NAT_1:53</a></i>;<br/>
<b>hence </b><a NAME="E5:113"/>
 <a href="pepin.html#K5" target="_self">Fermat</a> 3 <a href="nat_1.html#R1">divides</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">32 <a href="nat_1.html#K2">*</a> 0</span>)</span> <a href="nat_1.html#K1">+</a> 128</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="pepin.html#T7" target="_self">Th7</a></i>;<br/>


</div>
