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<a NAME="E1:49_1_1"/><span class="lab"><font color="Green" title="E36">P0</font></span>: 
<font color="Maroon" title="c1">p</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#D4" title="INT_2:def.4">INT_2:def 4</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">a</font> =  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> ;<br/>
<a NAME="E3:49_1_1"/><span class="lab"><font color="Green" title="E37">P2</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_1"><span class="lab"><font color="Green" title="E36">P0</font></span></a>, <a class="ref" href="int_3.html#T14" title="INT_3:th.14">INT_3:14</a></span>;<br/>
<font color="Maroon" title="c2">a</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> 2 = 
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p2">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p2">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="ec_pf_1.html#E26"><span class="lab"><font color="Green" title="E21">EXLm4</font></span></a></span>
<br/>.= 
 <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E5:49_1_1"/>
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <span class="p1">(<span class="default"><a href="ec_pf_1.html#NK2" title="EC_PF_1:NK.2">GF</a> <font color="Maroon" title="c1">p</font></span>)</span> is  <a href="ec_pf_1.html#V2" title="EC_PF_1:attr.2">quadratic_residue</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:49_1_1"><span class="lab"><font color="Green" title="E37">P2</font></span></a>, <a class="ref" href="ec_pf_1.html#T34" target="_self" title="EC_PF_1:th.34">QR1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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