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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: EULER_2:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">Number</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp; <font color="Olive" title="b2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1 &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="nat_d.html#K2" title="NAT_D:func.2">mod</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n</font> <a href="nat_d.html#K2" title="NAT_D:func.2">mod</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b2">m</font>,<font color="Olive" title="b3">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  holds <br/><font color="Olive" title="b1">a</font> <a href="nat_d.html#K2" title="NAT_D:func.2">mod</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</div></div>
