Stage: 4 Challenge Level: 
Find the largest integer which divides every member of the following sequence:
$$ 1^5-1,\ 2^5-2,\ 3^5-3,\cdots\ n^5-n.$$
Number theory. Factorisation (algebraic). Inequality/inequalities. Manipulating algebraic expressions/formulae. Common factors. Visualising. Polynomials. Generalising. Factors and multiples. Mathematical reasoning & proof.
Published October 2001.
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