Problem 2

Part of 1992 Bulgaria National Olympiad

Problems(1)

no arith. seq. of 41 terms in 1904-subset of [1992]

Source: Bulgaria 1992 P2

Prove that there exists

1904

-element subset of the set

\{1,2,\ldots,1992\}

, which doesn’t contain an arithmetic progression consisting of

41

terms. (Ivan Tonov)