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Only consecutive terms are coprime

Source: 7th RMM 2015, Problem 1

February 28, 2015
number theoryrelatively primeRMMRMM 2015

Problem Statement

Does there exist an infinite sequence of positive integers a1,a2,a3,...a_1, a_2, a_3, . . . such that ama_m and ana_n are coprime if and only if mn=1|m - n| = 1?