<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: PYTHTRIP:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">m</font>, <font color="Olive" title="b5">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">n</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b4">m</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <font color="Olive" title="b5">n</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">n</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a>  ;<br/></div></div>
