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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E16">Th16</font></span>: <a NAME="T16"><span class="comment"><font color="firebrick">:: INT_5:16</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 2 holds <br/> ex <font color="Olive" title="b2">fp</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b2">fp</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">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 &amp; (  for <font color="Olive" title="b3">d</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">fp</font> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b2">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">d</font></span>)</span> <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 ) &amp; (  for <font color="Olive" title="b3">d</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">fp</font> holds <br/><font color="Olive" title="b2">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">d</font> <a href="int_5.html#R1" title="INT_5:pred.1">is_quadratic_residue_mod</a> <font color="Olive" title="b1">p</font> ) &amp; (  for <font color="Olive" title="b3">d</font>, <font color="Olive" title="b4">e</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">d</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">fp</font> &amp; <font color="Olive" title="b4">e</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">fp</font> &amp; <font color="Olive" title="b3">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">e</font> holds <br/> not <font color="Olive" title="b2">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b3">d</font>,<font color="Olive" title="b2">fp</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b4">e</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>
