I don&#x27;t understand. The end of the proof says <i>r&#x2F;p</i> is a fraction, presumably because <i>r</i> must be an integer. But why must <i>r</i> be an integer?<p>There seems to be an implicit assumption that <i>m</i> is an integer, but the explicit assumptions only give the much weaker statement that &quot;<i>m</i> is not a perfect square&quot;.