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<div><span class="kw">theorem </span><a NAME="T19"><span class="comment"><font color="firebrick">:: NUMBER12:19</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b3">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b4">i</font> where <font color="Olive" title="b4">i</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : <span class="p1">(<span class="default"><a href="number06.html#K1" title="NUMBER06:func.1">ArProg</a> (<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font>)</span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Olive" title="b4">i</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  </span> } </span>  holds <br/>( <font color="Olive" title="b3">A</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  iff <font color="Olive" title="b1">m</font> <a href="int_5.html#R1" title="INT_5:pred.1">is_quadratic_residue_mod</a> <font color="Olive" title="b2">n</font> )</div></div>
