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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">n</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  &amp;  not <font color="Maroon" title="c1">n</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  implies <font color="Maroon" title="c1">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:34_1_1"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
( <font color="Maroon" title="c1">n</font> is  <a href="pythtrip.html#V1" title="PYTHTRIP:attr.1">square</a>  &amp;  not <font color="Maroon" title="c1">n</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c2">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:34_1_1"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="square_1.html#K3" title="SQUARE_1:func.3">^2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pythtrip.html#D3" title="PYTHTRIP:def.3">PYTHTRIP:def 3</a></span>;<br/>
<a NAME="E4:34_1_1"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<font color="Maroon" title="c2">m</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:34_1_1"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="wsierp_1.html#T1" title="WSIERP_1:th.1">WSIERP_1:1</a></span>;<br/>
<a NAME="E5:34_1_1"/>
( <font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  &amp; <font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="square_1.html#K5" title="SQUARE_1:func.5">^2</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:34_1_1"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E3:34_1_1"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="nat_2.html#T28" title="NAT_2:th.28">NAT_2:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:34_1_1"/>
<font color="Maroon" title="c1">n</font> is  <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34_1_1"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="moebius1.html#T20" target="_self" title="MOEBIUS1:th.20">Th20</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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