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<b>let </b><font color="Maroon" title="c1">m</font>, <font color="Maroon" title="c2">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="E1:37"/><i><font color="Green" title="E27">A1</font></i>: 
not <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 ;<br/>

<b>assume </b><a NAME="E2:37"/>
<font color="Maroon" title="c1">m</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><b> such that </b><br/><a NAME="E4:37"/><i><font color="Green" title="E28">A2</font></i>: 
<font color="Maroon" title="c3">p</font> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font>
 <b>by </b><i><a class="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></i>;<br/>
<a NAME="E5:37"/>
<font color="Maroon" title="c3">p</font> <a href="newton.html#K16" title="NEWTON:func.16">|^</a> 2 <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c1">m</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c2">n</font>
 
<b>by </b><i><a class="txt" href="moebius1.html#E4:37"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="nat_d.html#T9" title="NAT_D:th.9">NAT_D:9</a></i>;<br/>
<b>hence </b><a NAME="E6:37"/>
contradiction
 <b>by </b><i><a class="txt" href="moebius1.html#E1:37"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></i>;<br/>


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