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<b>let </b><font color="Maroon">n</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:35_1_1"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">n</font> is <a href="pythtrip.html#V1">square</a> &amp; not <font color="Maroon">n</font> is <a href="realset1.html#V1">trivial</a> )
 ;<br/>

<b>then consider </b><font color="Maroon">m</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="ref" href="pythtrip.html#D3">PYTHTRIP:def 3</a></i>;<br/>
<a NAME="E4:35_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i>, , <a class="ref" href="square_1.html#T59">SQUARE_1:59</a>, <a class="ref" href="nat_2.html#T30">NAT_2:30</a></i>;<br/>
<a NAME="E5:35_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 
<b>by </b><i>, , <a class="ref" href="square_1.html#T60">SQUARE_1:60</a>, <a class="ref" href="nat_2.html#T30">NAT_2:30</a></i>;<br/>
<a NAME="E6:35_1_1"/>
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">m</font>
 
<b>by </b><i>, <a class="ref" href="square_1.html#D3">SQUARE_1:def 3</a></i>;<br/>
<a NAME="E7:35_1_1"/><b>then </b>
<font color="Maroon">m</font> <a href="newton.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="wsierp_1.html#T2">WSIERP_1:2</a></i>;<br/>
<b>hence </b><a NAME="E8:35_1_1"/>
<font color="Maroon">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 <b>by </b><i>, , </i>;<br/>


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