MathDB

13

Part of 1969 IMO Shortlist

Problems(1)

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

Source:

9/29/2010
(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?
modular arithmeticnumber theoryDivisibilityAdditive Number TheoryIMO ShortlistIMO Longlist