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<b>let </b><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">k</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="E1:3"/><i><font color="Green" title="E4">A1</font></i>: 
( <font color="Maroon" title="c2">j</font> is <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> &amp; <font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c1">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">a</font> being    <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> <b> such that </b><br/><a NAME="E3:3"/><i><font color="Green" title="E5">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font>
 <b>by </b><i><a class="txt" href="idea_1.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c5">a'</font> being    <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> <b> such that </b><br/><a NAME="E5:3"/><i><font color="Green" title="E6">A3</font></i>: 
<font color="Maroon" title="c5">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">j</font>
 ;<br/>
<b>take </b>
<font color="Maroon" title="c5">a'</font>
;<br/>

<b>thus </b><a NAME="E6:3"/>
( <span class="p1">(<span class="default"><font color="Maroon" title="c5">a'</font> <a href="nat_1.html#K4" title="NAT_1:func.4">*</a> <font color="Maroon" title="c1">i</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Maroon" title="c2">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c5">a'</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> )
 <b>by </b><i><a class="txt" href="idea_1.html#E1:3"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="idea_1.html#E3:3"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="idea_1.html#E5:3"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="euler_2.html#T10" title="EULER_2:th.10">EULER_2:10</a>, <a class="ref" href="nat_d.html#T1" title="NAT_D:th.1">NAT_D:1</a></i>;<br/>


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