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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>assume </b><a NAME="E1:36"/><i><font color="Green" title="E26">A1</font></i>: 
not <font color="Maroon" title="c1">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 ;<br/>

<b>given </b><font color="Maroon" title="c2">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><b> such that </b><a NAME="E3:36"/><i><font color="Green" title="E27">A2</font></i>: 
<font color="Maroon" title="c2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 ;<br/>

<a NAME="E4:36"/>
<font color="Maroon" title="c2">p</font> <a href="nat_3.html#K11" title="NAT_3:func.11">|-count</a> <font color="Maroon" title="c1">n</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 1 <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1
 
<b>by </b><i><a class="txt" href="moebius1.html#E3:36"><i><font color="Green" title="E27">A2</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<a NAME="E5:36"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="moebius1.html#E1:36"><i><font color="Green" title="E26">A1</font></i></a>, <a class="ref" href="moebius1.html#T9" target="_self" title="MOEBIUS1:th.9">Th9</a>, <a class="ref" href="moebius1.html#T21" target="_self" title="MOEBIUS1:th.21">Th21</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
contradiction
 <b>by </b><i><a class="txt" href="moebius1.html#E1:36"><i><font color="Green" title="E26">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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