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<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="E1:36"/><i><font color="Green">E41</font></i>: 
not <font color="Maroon">n</font> is <a href="moebius1.html#V1" target="_self">square-containing</a>
 ;<br/>

<b>given </b><font color="Maroon">p</font> being   <a href="newton.html#NM1">Prime</a><b> such that </b><a NAME="E2:36"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">p</font> <a href="nat_3.html#K11">|-count</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1
 ;<br/>

<a NAME="E3:36"/>
<font color="Maroon">p</font> <a href="nat_3.html#K11">|-count</a> <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 1 <a href="binop_2.html#K23">+</a> 1
 
<b>by </b><i>, <a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E4:36"/><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">n</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:36"/>
contradiction
 <b>by </b><i>, </i>;<br/>


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