Take any pair of two digit numbers  <i>ab</i>  and  <i>cd</i>  where, without loss of
generality,


 <i>ab</i> &#x003E; <i>cd</i> . Form two 4 digit numbers  <i>abcd</i>  and  <i>cdab</i>  and calculate:





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&#x00A0;<i>abcd</i><sup>2</sup>&#8722;<i>cdab</i><sup>2</sup>
<div class="hrcomp"><hr noshade="noshade" size="1"/><i>ab</i><sup>2</sup>&#8722;<i>cd</i><sup>2</sup><br /></td><td nowrap="nowrap" align="center">
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Repeat this with other choices of <i>ab</i> and <i>cd</i>. There is a common feature of
all the answers. What is it? Why does this occur? Generalise this to <i>n</i>
digits for other values of <i>n</i>.