Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Find the largest integer which divides every member of the following sequence:

$$ 1^5-1,\ 2^5-2,\ 3^5-3,\cdots\ n^5-n.$$

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NRICH is part of the family of activities in the Millennium Mathematics Project.

NRICH is part of the family of activities in the Millennium Mathematics Project.