Problem

Source: Singapore Senior Math Olympiad 2017 2nd Round p5 SMO

Tags: Arithmetic Progression, algebra, combinatorics, Integers, Sequence, number theory



Given $7$ distinct positive integers, prove that there is an infinite arithmetic progression of positive integers $a, a + d, a + 2d,..$ with $a < d$, that contains exactly $3$ or $4$ of the $7$ given integers.