Find all functions $f : R^2 \to R$ that for all real numbers $x, y, z$ satisfies to the equation $f(f(x,z), f(z, y))= f(x, y) + z$
Problem
Source: 2019 Saudi Arabia IMO Training Test 4.2
Tags: functional, functional equation, algebra
Source: 2019 Saudi Arabia IMO Training Test 4.2
Tags: functional, functional equation, algebra
Find all functions $f : R^2 \to R$ that for all real numbers $x, y, z$ satisfies to the equation $f(f(x,z), f(z, y))= f(x, y) + z$