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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: NAT_6:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  2 <a href="nat_6.html#V1" title="NAT_6:attr.1">_greater</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a> <br/>  for <font color="Olive" title="b2">s</font> being   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>   <a href="nat_6.html#M1" title="NAT_6:mode.1">Divisor</a> of <font color="Olive" title="b1">n</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1  st <font color="Olive" title="b2">s</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="square_1.html#K3" title="SQUARE_1:func.3">sqrt</a> <font color="Olive" title="b1">n</font> &amp;  ex <font color="Olive" title="b3">a</font> being   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM2" title="ORDINAL1:NM.2">number</a>  st <br/>( <font color="Olive" title="b3">a</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> <span class="p1">(<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>,1 <a href="int_1.html#R2" title="INT_1:pred.2">are_congruent_mod</a> <font color="Olive" title="b1">n</font> &amp; (  for <font color="Olive" title="b4">q</font> being   <a href="int_2.html#V1" title="INT_2:attr.1">prime</a>   <a href="nat_6.html#M1" title="NAT_6:mode.1">Divisor</a> of <font color="Olive" title="b2">s</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">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="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> <font color="Olive" title="b4">q</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) ) holds <br/><font color="Olive" title="b1">n</font> is  <a href="int_2.html#V1" title="INT_2:attr.1">prime</a> </div></div>
