IMO Shortlist 1969 problem 25


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2. travnja 2012.
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(GBR 2) 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 expressible 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).
Izvor: Međunarodna matematička olimpijada, shortlist 1969