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Strictly Increasing Sequences

Source: Junior Olympiad of Malaysia Shortlist 2015 N3 (JOM P4)

July 17, 2015
number theory

Problem Statement

Given a natural number n≥3n\ge 3, determine all strictly increasing sequences a1<a2<⋯<ana_1<a_2<\cdots<a_n such that gcd(a1,a2)=1\text{gcd}(a_1,a_2)=1 and for any pair of natural numbers (k,m)(k,m) satisfy n≥m≥3n\ge m\ge 3, m≥km\ge k, a1+a2+⋯+amak\frac{a_1+a_2+\cdots +a_m}{a_k} is a positive integer.
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