MathDB

12

Part of 2015 Ukraine Team Selection Test

Problems(1)

set A, subset of {1,2,...,n}, contains a three-element arithmetic sequence

Source: Ukraine TST 2015 p12

5/2/2020
For a given natural nn, we consider the set A⊂{1,2,...,n}A\subset \{1,2, ..., n\}, which consists of at least [n+12]\left[\frac{n+1}{2}\right] items. Prove that for n≥2015n \ge 2015 the set AA contains a three-element arithmetic sequence.
Setsarithmetic sequenceSubsetalgebra