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<div><span class="kw">theorem </span><a NAME="T15"><span class="comment"><font color="firebrick">:: GR_CY_3:15</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">p</font> being   <a href="gr_cy_3.html#V1" title="GR_CY_3:attr.1">Safe</a>  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  ex <font color="Olive" title="b2">q</font> being   <a href="gr_cy_3.html#V2" title="GR_CY_3:attr.2">Sophie_Germain</a>  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a> ex <font color="Olive" title="b3">H1</font>, <font color="Olive" title="b4">H2</font>, <font color="Olive" title="b5">Hq</font>, <font color="Olive" title="b6">H2q</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of  <a href="int_7.html#K3" title="INT_7:func.3">Z/Z*</a> <font color="Olive" title="b1">p</font> st <br/>(  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b3">H1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b4">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b5">Hq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">q</font> &amp;  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b6">H2q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b2">q</font> &amp; (  for <font color="Olive" title="b7">H</font> being   <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of  <a href="int_7.html#K3" title="INT_7:func.3">Z/Z*</a> <font color="Olive" title="b1">p</font>  holds <br/>( <font color="Olive" title="b7">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b3">H1</font> or <font color="Olive" title="b7">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b4">H2</font> or <font color="Olive" title="b7">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b5">Hq</font> or <font color="Olive" title="b7">H</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a> <font color="Olive" title="b6">H2q</font> ) ) )</div></div>
