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<a NAME="E1:113"/>
<span class="p1">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
;<br/>
<a NAME="E2:113"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A1</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></span>;<br/>
<a NAME="E3:113"/>
1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 256</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
;<br/>
<a NAME="E4:113"/><span class="kw">then </span>
1 <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></span>;<br/>
<a NAME="E5:113"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">64 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p4">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 128</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:113"><span class="lab"><font color="Green" title="E90">A1</font></span></a>, <a class="txt" href="pepin.html#E113"><span class="lab"><font color="Green" title="E87">Lm47</font></span></a>, <a class="ref" href="euler_2.html#T8" title="EULER_2:th.8">EULER_2:8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:113"/>
 <a href="pepin.html#K5" title="PEPIN:func.5">Fermat</a> 4 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <span class="p1">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">64 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p3">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 128</span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pepin.html#T7" target="_self" title="PEPIN:th.7">Th7</a>, <a class="ref" href="nat_d.html#T6" title="NAT_D:th.6">NAT_D:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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