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<b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:66"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">p</font> is <a href="int_2.html#V1">prime</a> &amp; <font color="Maroon">i</font>,<font color="Maroon">p</font> <a href="int_2.html#R2">are_relative_prime</a>  )
 ;<br/>

<a NAME="E2:66"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="wsierp_1.html#K2">|^</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="binarith.html#K3">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K6">mod</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i/>;<br/>
<a NAME="E3:66"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="int_2.html#D5">INT_2:def 5</a></i>;<br/>
<a NAME="E4:66"/><b>then </b>
<font color="Maroon">p</font> <a href="xcmplx_0.html#K6">-</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K6">-</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T11">XREAL_1:11</a></i>;<br/>
<a NAME="E5:66"/><b>then </b>
<font color="Maroon">p</font> <a href="binarith.html#K3">-'</a> 1 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="binarith.html#D3">BINARITH:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:66"/>
 <a href="pepin.html#K4" target="_self">order</a> <font color="Maroon">i</font>,<font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">p</font> <a href="binarith.html#K3">-'</a> 1
 <b>by </b><i>, , <a class="txt" href="pepin.html#E4"><i><font color="Green">Lemma54</font></i></a>, <a class="txt" href="pepin.html#E3:66"><i><font color="Green">E49</font></i></a></i>;<br/>


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