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<b>let </b><font color="Maroon" title="c1">a</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>  st <font color="Maroon" title="c1">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 holds <br/> <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> </span>)</span>,<font color="Olive" title="b1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/><b>let </b><font color="Maroon" title="c2">p</font> be   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 implies  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> </span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>



<b>assume </b><a NAME="E1:33"/>
<font color="Maroon" title="c1">a</font> <a href="int_2.html#K3" title="INT_2:func.3">gcd</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> </span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1</span><br/>

<a NAME="E2:33"/><b>then </b>
<font color="Maroon" title="c1">a</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a>  <a href="int_5.html#R1" title="INT_5:pred.1">is_quadratic_residue_mod</a> <font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="int_5.html#T9" target="_self" title="INT_5:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:33"/>
 <a href="int_5.html#K2" title="INT_5:func.2">Lege</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="pepin.html#K2" title="PEPIN:func.2">^2</a> </span>)</span>,<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="int_5.html#D3" target="_self" title="INT_5:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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