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<b>let </b><font color="Maroon">m</font> be  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be  non <a href="xboole_0.html#V1">zero</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><a NAME="E1:51"/>
not <font color="Maroon">m</font>,<font color="Maroon">n</font> <a href="int_2.html#R2">are_relative_prime</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being  <a href="int_2.html#V1">prime</a> <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:51"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> &amp; <font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">n</font> )
 <b>by </b><i><a class="ref" href="pythtrip.html#D2">PYTHTRIP:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">p</font> as  <a href="int_2.html#V1">prime</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E5:51"/>
<font color="Maroon">p</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">p</font> <a href="nat_1.html#R1">divides</a> <font color="Maroon">m</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font>
 
<b>by </b><i>, <a class="ref" href="nat_3.html#T1">NAT_3:1</a></i>;<br/>
<a NAME="E6:51"/><b>then </b>
<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="binop_2.html#K24">*</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="wsierp_1.html#T2">WSIERP_1:2</a></i>;<br/>
<a NAME="E7:51"/><b>then </b>
<font color="Maroon">m</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:51"/>
 <a href="moebius1.html#K2" target="_self">Moebius</a> <span class="p1">(<span class="default"><font color="Maroon">m</font> <a href="binop_2.html#K24">*</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i/>;<br/>


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