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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a></span><br/>

<a NAME="E1:78"/><i><font color="Green" title="E60">A1</font></i>: 
<span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1
 
<b>by </b><i><a class="ref" href="binarith.html#D3" title="BINARITH:def.3">BINARITH:def 3</a></i>;<br/>
<a NAME="E2:78"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="pepin.html#E80"><i><font color="Green" title="E56">Lm17</font></i></a></i>;<br/>
<a NAME="E3:78"/><b>then </b>
<span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> 1 is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 
<b>by </b><i><a class="ref" href="nat_2.html#T23" title="NAT_2:th.23">NAT_2:23</a></i>;<br/>
<b>hence </b><a NAME="E4:78"/>
not  <a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> <font color="Maroon" title="c1">n</font> is <a href="abian.html#V1" title="ABIAN:attr.1">even</a>
 <b>by </b><i><a class="txt" href="pepin.html#E1:78"><i><font color="Green" title="E60">A1</font></i></a>, <a class="ref" href="pepin.html#T16" target="_self" title="PEPIN:th.16">Th16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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