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<b>let </b><font color="Maroon">k</font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:76_1"/>
( <font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 or <font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_1"><b>suppose </b></a><a NAME="E1:76_1_1"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 ;<br/><div class="add"><b>hence </b><a NAME="E2:76_1_1"/>
( <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">m</font> iff <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a>  <a href="prepower.html#K1">abs</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="76_1_2"><b>suppose </b></a><a NAME="E1:76_1_2"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:76_1_2"/><b>then </b>
 <a href="prepower.html#K1">abs</a> <font color="Maroon">m</font> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">m</font>
 <b>by </b><i><a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/><b>hence </b><a NAME="E3:76_1_2"/>
( <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a> <font color="Maroon">m</font> iff <font color="Maroon">k</font> <a href="int_1.html#R2">divides</a>  <a href="prepower.html#K1">abs</a> <font color="Maroon">m</font> )
 <b>by </b><i><a class="ref" href="int_2.html#T14">INT_2:14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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