IMO 2007 Shortlist N3

Let X be a set of 10000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset Y of X ...

imomathematicsolympiadshortlistnumber-theory

IMO 2007 Shortlist N3

Category: Number Theory

Problem

Let X be a set of 10000 integers, none of them is divisible by 47. Prove that there exists a 2007-element subset Y of X such that a − b + c − d + e is not divisible by 47 for any a,b,c,d,e ∈ Y . (Netherlands)