Question 49
Determine all nonzero integers $a$ for which there exist functions $f,g:\mathbb Q\to\mathbb Q$ satisfying
$$
f(x+g(y))=g(x)+f(y)+ay\qquad\text{for all }x,y\in\mathbb Q.
$$
Determine all such functions.
$$
f(x+g(y))=g(x)+f(y)+ay\qquad\text{for all }x,y\in\mathbb Q.
$$
Determine all such functions.