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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E21">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: INT_5:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">a</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/>  for <font color="Olive" title="b2">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Olive" title="b2">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 &amp; <font color="Olive" title="b1">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  not <font color="Olive" title="b1">a</font> <a href="int_5.html#R1" title="INT_5:pred.1">is_quadratic_residue_mod</a> <font color="Olive" title="b2">p</font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">p</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span> <a href="nat_d.html#K3" title="NAT_D:func.3">div</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 1</span>)</span> <a href="int_1.html#K5" title="INT_1:func.5">mod</a> <font color="Olive" title="b2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> </div></div>
