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<b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<a NAME="E1:75"/><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> <font color="Maroon">n</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 <a href="hidden.html#R1">=</a> 2 <a href="wsierp_1.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="binarith.html#T39">BINARITH:39</a></i>;<br/>
<a NAME="E2:75"/>
2 <a href="nat_1.html#K6">mod</a> 2 <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T77">NAT_1:77</a></i>;<br/>
<a NAME="E3:75"/><b>then </b><i><font color="Green">E45</font></i>: 
2 is <a href="abian.html#V1">even</a>
 
<b>by </b><i><a class="ref" href="nat_2.html#T23">NAT_2:23</a></i>;<br/>
<a NAME="E4:75"/>
2 <a href="wsierp_1.html#K2">|^</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/>
<a NAME="E5:75"/><b>then </b>
<span class="p1">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> <font color="Maroon">n</font></span>)</span> <a href="binarith.html#K3">-'</a> 1 is <a href="abian.html#V1">even</a>
 
<b>by </b><i><a class="ref" href="pepin.html#T4" target="_self">Th4</a>, , </i>;<br/>
<b>hence </b><a NAME="E6:75"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pepin.html#K5" target="_self">Fermat</a> <font color="Maroon">n</font></span>)</span> <a href="binarith.html#K3">-'</a> 1</span>)</span> <a href="nat_1.html#K6">mod</a> 2 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="nat_2.html#T23">NAT_2:23</a></i>;<br/>


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