IMO 2015 Shortlist A5

Let 2Z 1 denote the set of odd integers. Find all functions f : Z Ñ 2Z 1 satisfying f x fpxq y ˘ f x ´ fpxq ´ y ˘ “ fpx ...

IMO 2015 Shortlist A5

Category: Algebra

Problem

Let 2Z 1 denote the set of odd integers. Find all functions f : Z Ñ 2Z 1 satisfying f x fpxq y ˘ f x ´ fpxq ´ y ˘ “ fpx yq ` fpx ´ yq for every x,y P Z. (U.S.A.)