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0 < a_{n+1} - a_n \leq 2001

Source: Vietnam TST 2001 for the 42th IMO, problem 6

June 26, 2005
algebra unsolvedalgebranumber theorypen

Problem Statement

Let a sequence {an}\{a_n\}, n∈N∗n \in \mathbb{N}^{*} given, satisfying the condition 0<an+1−an≤20010 < a_{n+1} - a_n \leq 2001 for all n∈N∗n \in \mathbb{N}^{*} Show that there are infinitely many pairs of positive integers (p,q)(p, q) such that p<qp < q and apa_p is divisor of aqa_q.
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