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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: GR_CY_2:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">G</font> being   <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a><br/>  for <font color="Olive" title="b4">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b3">G</font>  st <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> holds <br/>( <font color="Olive" title="b3">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_4.html#K5" title="GROUP_4:func.5">gr</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b4">a</font> <a href="group_1.html#K5" title="GROUP_1:func.5">|^</a> <font color="Olive" title="b1">k</font></span>)</span></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> iff <font color="Olive" title="b1">k</font> <a href="nat_d.html#K6" title="NAT_D:func.6">gcd</a> <font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</div></div>
