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How many noughts are at the end of these giant numbers?

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Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.

Common Divisor

Age 14 to 16 Challenge Level:

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

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