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<b>let </b><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> ;<br/>

<b>assume </b><a NAME="E1:35_1_1"/><i><font color="Green" title="E25">A1</font></i>: 
( <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="realset1.html#V1" title="REALSET1:attr.1">trivial</a> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green" title="E26">A2</font></i>: 
<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> 
 <b>by </b><i><a class="ref" href="pythtrip.html#D3" title="PYTHTRIP:def.3">PYTHTRIP:def 3</a></i>;<br/>
<a NAME="E4:35_1_1"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 
<b>by </b><i><a class="txt" href="moebius1.html#E1:35_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="moebius1.html#E3:35_1_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="square_1.html#T59" title="SQUARE_1:th.59">SQUARE_1:59</a>, <a class="ref" href="nat_2.html#T30" title="NAT_2:th.30">NAT_2:30</a></i>;<br/>
<a NAME="E5:35_1_1"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 0
 
<b>by </b><i><a class="txt" href="moebius1.html#E1:35_1_1"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="moebius1.html#E3:35_1_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="square_1.html#T60" title="SQUARE_1:th.60">SQUARE_1:60</a>, <a class="ref" href="nat_2.html#T30" title="NAT_2:th.30">NAT_2:30</a></i>;<br/>
<a NAME="E6:35_1_1"/>
<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="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">m</font>
 
<b>by </b><i><a class="txt" href="moebius1.html#E3:35_1_1"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="square_1.html#D3" title="SQUARE_1:def.3">SQUARE_1:def 3</a></i>;<br/>
<a NAME="E7:35_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="wsierp_1.html#T2" title="WSIERP_1:th.2">WSIERP_1:2</a></i>;<br/>
<b>hence </b><a NAME="E8:35_1_1"/>
<font color="Maroon" title="c1">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 <b>by </b><i><a class="txt" href="moebius1.html#E4:35_1_1"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="moebius1.html#E5:35_1_1"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="moebius1.html#T20" target="_self" title="MOEBIUS1:th.20">Th20</a></i>;<br/>


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