IMO 2024 Shortlist A4

Let Zą0 be the set of all positive integers. Determine all subsets S of t20 ,21 ,22 ,...u for which there exists a funct...

imomathematicsolympiadshortlistalgebra

IMO 2024 Shortlist A4

Category: Algebra

Problem

Let Zą0 be the set of all positive integers. Determine all subsets S of t20 ,21 ,22 ,...u for which there exists a function f : Zą0 Ñ Zą0 such that S “ tfpa ` bq ´ fpaq ´ fpbq | a,b P Zą0u. (Thailand)