<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green" title="E9">A1</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:18_1"/>
( <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> or <font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">n</font> )
 </span><b>by </b><i><a class="txt" href="pythtrip.html#E1:18"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="square_1.html#T109" title="SQUARE_1:th.109">SQUARE_1:109</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1"><b>suppose </b></a><a NAME="E1:18_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:18_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_2"><b>suppose </b></a><a NAME="E1:18_1_2"/><i><font color="Green" title="E10">A2</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Maroon" title="c2">n</font>
 ;<br/><div class="add"><a NAME="E2:18_1_2"/>
( <font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 &amp; <font color="Maroon" title="c2">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 ;<br/><a NAME="E3:18_1_2"/><b>then </b>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 0
 <b>by </b><i><a class="txt" href="pythtrip.html#E1:18_1_2"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/><b>hence </b><a NAME="E4:18_1_2"/>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font>
 <b>by </b><i><a class="txt" href="pythtrip.html#E1:18_1_2"><i><font color="Green" title="E10">A2</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
