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<div><span class="kw">theorem </span><a NAME="T45"><span class="comment"><font color="firebrick">:: PEPIN:45</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">k1</font>, <font color="Olive" title="b5">k2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b2">p</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  &amp; <font color="Olive" title="b3">q</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  &amp; <font color="Olive" title="b2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">p</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b3">q</font> &amp; <font color="Olive" title="b4">k1</font>, <a href="euler_1.html#K1" title="EULER_1:func.1">Euler</a> <font color="Olive" title="b1">n</font> <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a>  &amp; <span class="p1">(<span class="default"><font color="Olive" title="b4">k1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b5">k2</font></span>)</span> <a href="nat_d.html#K4" title="NAT_D:func.4">mod</a> <span class="p1">(<span class="default"><a href="euler_1.html#K1" title="EULER_1:func.1">Euler</a> <font color="Olive" title="b1">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> for <font color="Olive" title="b6">m</font> being    <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="b6">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">n</font> holds <br/> <a href="pepin.html#K2" title="PEPIN:func.2">Crypto</a> (<span class="p1">(<span class="default"><a href="pepin.html#K2" title="PEPIN:func.2">Crypto</a> (<font color="Olive" title="b6">m</font>,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b4">k1</font>)</span>)</span>,<font color="Olive" title="b1">n</font>,<font color="Olive" title="b5">k2</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">m</font></div></div>
