IMO 1969 LL CZS13

Let p be a prime odd number. Is it possible to find p−1 natural

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IMO 1969 LL CZS13

Origin: CZS

Problem

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