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<b>let </b><font color="Maroon" title="c1">n</font> be  non <a href="xxreal_0.html#NV2" title="XXREAL_0:NV.2">zero</a> <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="moebius1.html#K6" title="MOEBIUS1:func.6">Radical</a> <font color="Maroon" title="c1">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a></span><br/>

<b>assume </b><a NAME="E1:84"/>
 <a href="moebius1.html#K6" title="MOEBIUS1:func.6">Radical</a> <font color="Maroon" title="c1">n</font> is <a href="moebius1.html#V1" title="MOEBIUS1:attr.1">square-containing</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c2">p</font> being   <a href="newton.html#NM1" title="NEWTON:NM.1">Prime</a><b> such that </b><br/><a NAME="E3:84"/><i><font color="Green" title="E54">A1</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>  <a href="moebius1.html#K6" title="MOEBIUS1:func.6">Radical</a> <font color="Maroon" title="c1">n</font>
 <b>by </b><i><a class="ref" href="moebius1.html#D1" target="_self" title="MOEBIUS1:def.1">Def1</a></i>;<br/>
<b>thus </b><a NAME="E4:84"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="moebius1.html#E71"><i><font color="Green" title="E52">Lm3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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