IMO 1989 LL IND51

Let t(n), for n = 3, 4, 5, . . ., represent the number of distinct,

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IMO 1989 LL IND51

Origin: IND

Problem

Let t(n), for n = 3, 4, 5, . . ., represent the number of distinct, incongruent, integer-sided triangles whose perimeter is n; e.g., t(3) = 1. Prove that t(2n −1) −t(2n) = n  or n 6 + 1  .