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<a NAME="E1:103"/><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default">123 <a href="nat_1.html#K2">*</a> 503</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default">123 <a href="nat_1.html#K2">*</a> 503</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">325 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default">241 <a href="nat_1.html#K2">*</a> 241</span>)</span></span>)</span> <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"><span class="p2">(<span class="default">14 <a href="nat_1.html#K2">*</a> 1367</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
;<br/>
<span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> 64</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> 4</span>)</span> = 
<span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default">32 <a href="nat_1.html#K1">+</a> 32</span>)</span></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> 4</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> 32</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> 32</span>)</span></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> 4</span>)</span>
<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">123 <a href="nat_1.html#K2">*</a> 503</span>)</span> <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default">123 <a href="nat_1.html#K2">*</a> 503</span>)</span></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> 4</span>)</span>
<b>by </b><i><a class="txt" href="pepin.html#E109"><i><font color="Green">Lemma86</font></i></a>, <a class="ref" href="euler_2.html#T11">EULER_2:11</a></i>
<br/>.= 
<span class="p1">(<span class="default">14 <a href="nat_1.html#K2">*</a> 1367</span>)</span> <a href="nat_1.html#K1">+</a> 1
<b>by </b><i><a class="txt" href="pepin.html#E1:103"><i><font color="Green">E88</font></i></a>, <a class="ref" href="pepin.html#T59" target="_self">Th59</a>, <a class="ref" href="nat_1.html#D2">NAT_1:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E3:103"/>
<span class="p1">(<span class="default">3 <a href="wsierp_1.html#K2">|^</a> 64</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> 4</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">14 <a href="nat_1.html#K2">*</a> 1367</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/>


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