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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E32">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: NAT_6:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being  2 <a href="nat_6.html#V1" title="NAT_6:attr.1">_greater</a>  <a href="int_2.html#NM1" title="INT_2:NM.1">Prime</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>  st <font color="Olive" title="b2">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/><font color="Olive" title="b2">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">p</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> 2</span>)</span>, <a href="nat_6.html#K1" title="NAT_6:func.1">LegendreSymbol</a> (<font color="Olive" title="b2">a</font>,<font color="Olive" title="b1">p</font>) <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b1">p</font></div></div>
