IMO 1969 LL GBR25

Let a, b, x, y be positive integers such that a and b have no

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IMO 1969 LL GBR25

Origin: GBR

Problem

Let a, b, x, y be positive integers such that a and b have no common divisor greater than 1. Prove that the largest number not ex- pressible in the form ax + by is ab −a −b. If N(k) is the largest number not expressible in the form ax + by in only k ways, find N(k).