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<a NAME="E1:107"/><span class="lab"><font color="Green" title="E84">A1</font></span>: 
<span class="p1">(<span class="default">32 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 257</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">32 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 257</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">1031 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <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></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default">81 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 809</span>)</span>
 
;<br/>
<span class="p1">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 4</span>)</span></span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p1">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 4</span>)</span></span>)</span> = 
3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <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> 4</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 4</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="newton.html#T13" title="NEWTON:th.13">NEWTON:13</a></span>
<br/>.= 
3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> 2048

;<br/>
<span class="kw">then </span><span class="p1">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 8</span>)</span></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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">32 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 257</span>)</span> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <span class="p2">(<span class="default">32 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 257</span>)</span></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="pepin.html#E108"><span class="lab"><font color="Green" title="E82">Lm42</font></span></a>, <a class="ref" href="pepin.html#T59" target="_self" title="PEPIN:th.59">Th59</a>, <a class="ref" href="euler_2.html#T11" title="EULER_2:th.11">EULER_2:11</a></span>
<br/>.= 
81 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 809
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:107"><span class="lab"><font color="Green" title="E84">A1</font></span></a>, <a class="ref" href="nat_d.html#D2" title="NAT_D:def.2">NAT_D:def 2</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E4:107"/>
<span class="p1">(<span class="default">3 <a href="newton.html#K15" title="NEWTON:func.15">|^</a> <span class="p2">(<span class="default">256 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 8</span>)</span></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> 81 <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> 809
 ; <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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