MathDB
Set differences

Source: 2016 KMO Senior #8

November 12, 2016
combinatoricsProbabilistic Method

Problem Statement

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
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