IMO 1979 LL FIN19

For k = 1, 2, . . . consider the k-tuples (a1, a2, . . . , ak) of positive

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IMO 1979 LL FIN19

Origin: FIN

Problem

For k = 1, 2, . . . consider the k-tuples (a1, a2, . . . , ak) of positive integers such that a1 + 2a2 + \cdot \cdot \cdot + kak = 1979. Show that there are as many such k-tuples with odd k as there are with even k.