MathDB

8

Part of 2016 Korea National Olympiad

Problems(1)

Set differences

Source: 2016 KMO Senior #8

11/12/2016
A subset S∈{0,1,2,⋯ ,2000}S \in \{0, 1, 2, \cdots , 2000\} satisfies ∣S∣=401|S|=401.
Prove that there exists a positive integer nn such that there are at least 7070 positive integers xx such that x,x+n∈Sx, x+n \in S
combinatoricsProbabilistic Method