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<b>let </b><font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">q</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">qc</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> ;<br/>



<b>assume </b><a NAME="E1:71"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">qc</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 ;<br/>

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

<b>assume </b><a NAME="E2:71"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a>  <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="uniroots.html#K6" target="_self">cyclotomic_poly</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">qc</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">ni</font> = <font color="Maroon">n</font> as  non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  ;<br/>
<b>consider </b><font color="Maroon">k</font> being   <a href="int_1.html#NM1">Integer</a>, <font color="Maroon">l</font> being   <a href="int_1.html#NM1">Integer</a>;<br/>
<b>consider </b><font color="Maroon">y1</font> being   <a href="struct_0.html#NM1">Element</a> of <a href="complfld.html#K1">F_Complex</a> <b> such that </b><br/><a NAME="E6:71"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> &amp;  <a href="polynom4.html#K2">eval</a> <span class="p1">(<span class="default"><a href="uniroots.html#K4" target="_self">unital_poly</a> <a href="complfld.html#K1">F_Complex</a> ,<font color="Maroon">n</font></span>)</span>,<font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="uniroots.html#K5" target="_self">|^</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E7:71"/>
<font color="Maroon">j</font> <a href="int_1.html#R2">divides</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="uniroots.html#K5" target="_self">|^</a> <font color="Maroon">n</font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1
 <b>by </b><i>, , , </i>;<br/>


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