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2 <a href="int_1.html#R1" title="INT_1:pred.1">divides</a> <font color="Maroon" title="c1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="abian.html#D1" onmouseover="rs('abian/D1')" onmouseout="rh()">ABIAN:def 1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">k</font> being   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><span class="kw"> such that </span><br/><a NAME="E3:79_1_1"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
<font color="Maroon" title="c1">a</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="Maroon" title="c2">k</font>
 ;<br/>
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<font color="Maroon" title="c2">k</font>,1 <a href="int_2.html#R1" title="INT_2:pred.1">are_coprime</a> 
 
;<br/>
<a NAME="E5:79_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">k</font></span>)</span> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="int_2.html#K1" title="INT_2:func.1">|.</a><span class="default">2</span><a href="int_2.html#K1" title="INT_2:func.1">.|</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="int_2.html#T24" onmouseover="rs('int_2/T24')" onmouseout="rh()">INT_2:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:79_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="newton03.html#K2" title="NEWTON03:func.2">gcd</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:79_1_1"><span class="lab"><font color="Green" title="E16">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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