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<div><span class="kw">theorem </span><a NAME="T59"><span class="comment"><font color="firebrick">:: UNIROOTS:59</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">ni</font>, <font color="Olive" title="b3">q</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>   st <font color="Olive" title="b2">ni</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> &amp; <font color="Olive" title="b2">ni</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Olive" title="b1">n</font> holds <br/> for <font color="Olive" title="b4">qc</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>  st <font color="Olive" title="b4">qc</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">q</font> holds <br/> for <font color="Olive" title="b5">j</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b5">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom4.html#K2" title="POLYNOM4:func.2">eval</a> (<span class="p1">(<span class="default"><a href="uniroots.html#K5" title="UNIROOTS:func.5">cyclotomic_poly</a> <font color="Olive" title="b1">n</font></span>)</span>,<font color="Olive" title="b4">qc</font>) holds <br/><font color="Olive" title="b5">j</font> <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">q</font> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_1.html#K4" title="INT_1:func.4">div</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">q</font> <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <font color="Olive" title="b2">ni</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></div></div>
