Question 151
Find all functions such that $f: \mathbb{Z} \to \mathbb{Z}$ that satisfy the following two conditions:
1) $f(x + f(x + 2y)) = f(2x) + f(2y)$ for all integers $x, y$;
2) $f(0) = 2$.
1) $f(x + f(x + 2y)) = f(2x) + f(2y)$ for all integers $x, y$;
2) $f(0) = 2$.