MathDB
Twenty-nine of them form an arithmetic progression

Source: IMO LongList 1988, Mongolia 1, Problem 51 of ILL

November 3, 2005
combinatorics unsolvedcombinatorics

Problem Statement

The positive integer nn has the property that, in any set of nn integers, chosen from the integers 1,2,…,1988,1,2, \ldots, 1988, twenty-nine of them form an arithmetic progression. Prove that n>1788.n > 1788.
Back to ProblemsView on AoPS