<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: NTALGO_1:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">y</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b2">p</font> &amp; <span class="p1">(<span class="default"><a href="ntalgo_1.html#K2" title="NTALGO_1:func.2">ALGO_EXGCD</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">y</font>)</span>)</span> <a href="mcart_1.html#K3" title="MCART_1:func.3">`3_3</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ntalgo_1.html#K3" title="NTALGO_1:func.3">ALGO_INVERSE</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">p</font>)</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">x</font></span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b2">p</font></div></div>
