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 ...
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.)