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<div><span class="kw">theorem </span><a NAME="T51"><span class="comment"><font color="firebrick">:: MOEBIUS3:51</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">k</font>, <font color="Olive" title="b2">n</font> being   non  <a href="ordinal1.html#V8" title="ORDINAL1:attr.8">zero</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds <br/> ( <font color="Olive" title="b1">k</font> <a href="pepin.html#K1" title="PEPIN:func.1">^2</a>  <a href="nat_d.html#R1" title="NAT_D:pred.1">divides</a>  <a href="moebius3.html#K6" title="MOEBIUS3:func.6">SquarefreePart</a> <font color="Olive" title="b2">n</font> iff <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 ) <span class="kw">by</span> <span class="lab"><a class="txt" href="moebius3.html#E59"><span class="lab"><font color="Green" title="E35">Surprise</font></span></a>, <a class="ref" href="nat_d.html#T6" onmouseover="rs('nat_d/T6')" onmouseout="rh()">NAT_D:6</a></span>;<br/></div></div>
