MathDB

5

Part of 2017 Singapore Senior Math Olympiad

Problems(1)

arithmetic progression of a, a + d, a + 2d,.. with 3,4,7 of given numbers

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

3/26/2020
Given 77 distinct positive integers, prove that there is an infinite arithmetic progression of positive integers a,a+d,a+2d,..a, a + d, a + 2d,.. with a<da < d, that contains exactly 33 or 44 of the 77 given integers.
Arithmetic ProgressionalgebracombinatoricsIntegersSequencenumber theory