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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E56">Th54</font></span>: <a NAME="T54"><span class="comment"><font color="firebrick">:: NUMBER14:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">S</font> being    <a href="number14.html#M2" title="NUMBER14:mode.2">Sierp49FS</a> of <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">k</font><br/>  for <font color="Olive" title="b4">q</font> being   <a href="int_6.html#NM1" title="INT_6:NM.1">CR_Sequence</a>  st <font color="Olive" title="b4">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="number14.html#K6" title="NUMBER14:func.6">PrimeDivisorsFS</a> <font color="Olive" title="b1">m</font> holds <br/> ex <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font> being   <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">a</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Olive" title="b6">b</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b1">m</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <font color="Olive" title="b6">b</font>,<font color="Olive" title="b1">m</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <font color="Olive" title="b5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="number14.html#K2" title="NUMBER14:func.2">CRT</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b4">q</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b4">q</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">k</font></span>)</span> &amp; <font color="Olive" title="b6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="number14.html#K2" title="NUMBER14:func.2">CRT</a> (<font color="Olive" title="b3">S</font>,<font color="Olive" title="b4">q</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K19" title="RVSUM_1:func.19">Product</a> <font color="Olive" title="b4">q</font></span>)</span> )</div></div>
