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Determine whether there exists a pair (p, q) of naturals

Source: IMO LongList 1982 - P26

March 18, 2011
number theory unsolvednumber theory

Problem Statement

Let (an)n≥0(a_n)_{n\geq0} and (bn)n≥0(b_n)_{n \geq 0} be two sequences of natural numbers. Determine whether there exists a pair (p,q)(p, q) of natural numbers that satisfy p < q   \text{ and }   a_p \leq a_q, b_p \leq b_q.
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