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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: EULER_2:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">m</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <font color="Olive" title="b2">m</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <font color="Olive" title="b2">m</font></div></div>
