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DOTS Division

Stage: 4 Challenge Level: Challenge Level:1

Take any pair of two digit numbers $ ab $ and $ cd $ where, without loss of generality, $ ab> cd $. Form two 4 digit numbers $ abcd $ and $ cdab $ and calculate: \[\frac{abcd^2-cdab^2}{ab^2-cd^2}\] Repeat this with other choices of $ab$ and $cd$. There is a common feature of all the answers. What is it? Why does this occur? Generalise this to $n$ digits for other values of $n$.