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Finding p-1 numbers whose sum of squares is divisible by sum

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September 29, 2010
modular arithmeticnumber theoryDivisibilityAdditive Number TheoryIMO ShortlistIMO Longlist

Problem Statement

(CZS2)(CZS 2) Let pp be a prime odd number. Is it possible to find p−1p-1 natural numbers n+1,n+2,...,n+p−1n + 1, n + 2, . . . , n + p -1 such that the sum of the squares of these numbers is divisible by the sum of these numbers?
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