IMO 1974 LL SWE35

If p and q are distinct prime numbers, then there are integers

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IMO 1974 LL SWE35

Origin: SWE

Problem

If p and q are distinct prime numbers, then there are integers x0 and y0 such that 1 = px0 + qy0. Determine the maximum value of b −a, where a and b are positive integers with the following property: If a \leqt \leqb, and t is an integer, then there are integers x and y with 0 \leqx \leqq −1 and 0 \leqy \leqp −1 such that t = px + qy.