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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E38">Th40</font></span>: <a NAME="T40"><span class="comment"><font color="firebrick">:: NAT_6:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="nat_6.html#V2" title="NAT_6:attr.2">Proth</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>  iff  ex <font color="Olive" title="b2">a</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <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">n</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="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b1">n</font> )</div></div>
