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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>given </b><font color="Maroon" title="c2">p</font> being  non <a href="xxreal_0.html#NV4" title="XXREAL_0:NV.4">zero</a> <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <b> such that </b><a NAME="E2:27"/><i><font color="Green" title="E21">A1</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1
 <b>and </b><br/><a NAME="E3:27"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c2">p</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>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">r</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><b> such that </b><br/><a NAME="E5:27"/><i><font color="Green" title="E23">A3</font></i>: 
<font color="Maroon" title="c3">r</font> <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a> <font color="Maroon" title="c2">p</font>
 <b>by </b><i><a class="txt" href="moebius1.html#E2:27"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="moebius1.html#E5"><i><font color="Green" title="E3">Lm2</font></i></a></i>;<br/>
<a NAME="E6:27"/>
<font color="Maroon" title="c2">p</font> is    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13" title="ORDINAL1:def.13">ORDINAL1:def 13</a></i>;<br/>
<a NAME="E7:27"/><b>then </b>
<font color="Maroon" title="c3">r</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="c2">p</font> <a href="newton.html#K2" title="NEWTON:func.2">|^</a> 2
 
<b>by </b><i><a class="txt" href="moebius1.html#E5:27"><i><font color="Green" title="E23">A3</font></i></a>, <a class="ref" href="wsierp_1.html#T19" title="WSIERP_1:th.19">WSIERP_1:19</a></i>;<br/>
<a NAME="E8:27"/><b>then </b>
<font color="Maroon" title="c3">r</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">n</font>
 
<b>by </b><i><a class="txt" href="moebius1.html#E3:27"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="nat_d.html#T4" title="NAT_D:th.4">NAT_D:4</a></i>;<br/>
<b>hence </b><a NAME="E9:27"/>
<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="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></i>;<br/>


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