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<b>let </b><font color="Maroon">m</font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><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="E1:37"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 ;<br/>

<b>assume </b><a NAME="E2:37"/>
<font color="Maroon">m</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being   <a href="newton.html#NM1">Prime</a><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">p</font> <a href="wsierp_1.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font>
 <b>by </b><i/>;<br/>
<a NAME="E5:37"/>
<font color="Maroon">p</font> <a href="wsierp_1.html#K2">|^</a> 2 <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T56">NAT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E6:37"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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