IMO 1982 LL FRA26

Let (an)n\geq0 and (bn)n\geq0 be two sequences of natural numbers.

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IMO 1982 LL FRA26

Origin: FRA

Problem

Let (an)n\geq0 and (bn)n\geq0 be two sequences of natural numbers. Determine whether there exists a pair (p, q) of natural numbers that satisfy p < q and ap \leqaq, bp \leqbq.