IMO 1985 LL NET58

Prove that there are infinitely many pairs (k, N) of positive

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IMO 1985 LL NET58

Origin: NET

Problem

Prove that there are infinitely many pairs (k, N) of positive integers such that 1 + 2 + \cdot \cdot \cdot + k = (k + 1) + (k + 2) + \cdot \cdot \cdot + N.