51

Part of 1988 IMO Longlists

Problems(1)

Twenty-nine of them form an arithmetic progression

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

The positive integer

n

has the property that, in any set of

n

integers, chosen from the integers

1,2, \ldots, 1988,

twenty-nine of them form an arithmetic progression. Prove that

n > 1788.

combinatorics unsolvedcombinatorics