Common divisor

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
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Problem



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

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