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Equal sum elements for equal product indices

Source: Indonesian Mathematical Olympiad 2014 Day 2 Problem 5

September 4, 2014
number theory unsolvednumber theory

Problem Statement

A sequence of positive integers a1,a2,…a_1, a_2, \ldots satisfies ak+al=am+ana_k + a_l = a_m + a_n for all positive integers k,l,m,nk,l,m,n satisfying kl=mnkl = mn. Prove that if pp divides qq then ap≤aqa_p \le a_q.
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