IMO 1978 LL GBR22

Two nonzero integers x, y (not necessarily positive) are such

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IMO 1978 LL GBR22

Origin: GBR

Problem

Two nonzero integers x, y (not necessarily positive) are such that x + y is a divisor of x2 + y2, and the quotient x2+y2 x+y is a divisor of