IMO 1969 LL HUN34

Let a and b be arbitrary integers. Prove that if k is an integer

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IMO 1969 LL HUN34

Origin: HUN

Problem

Let a and b be arbitrary integers. Prove that if k is an integer not divisible by 3, then (a + b)2k + a2k + b2k is divisible by a2 + ab + b2.