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<div class="add">

<a NAME="E1:108"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default">32 <a href="nat_1.html#K2">*</a> 257</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default">32 <a href="nat_1.html#K2">*</a> 257</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">1031 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K2">*</a> 256</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">81 <a href="nat_1.html#K2">*</a> 809</span>)</span>
 
;<br/>
<a NAME="E2:108"/>
3 <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K2">*</a> 8</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span> = 
3 <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>
<br/>.= 
3 <a href="wsierp_1.html#K2">|^</a> 2048

;<br/>
<b>hence </b><a NAME="E2:108_1"/>
3 <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default">256 <a href="nat_1.html#K2">*</a> 8</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 4</span>)</span></span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>then </b><span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 8</span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 4</span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">32 <a href="nat_1.html#K2">*</a> 257</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">32 <a href="nat_1.html#K2">*</a> 257</span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 256</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="pepin.html#T28" target="_self">Th28</a>, <a class="txt" href="pepin.html#E5"><i><font color="Green">Lemma56</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
81 <a href="nat_1.html#K2">*</a> 809
<b>by </b><i><a class="ref" href="pepin.html#T31" target="_self">Th31</a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E4:108"/>
<span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K2">*</a> 8</span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> 4</span>)</span> <a href="hidden.html#R1">=</a> 81 <a href="nat_1.html#K2">*</a> 809
 ;<br/>


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