MathNet 2019-part-03 — 184 problems (EN–VI) Question 66

Let $\mathbb{Z}$ be the set of integers. Determine all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that, for all integers $a$ and $b$,
$$
f(2a) + 2f(b) = f(f(a+b)).
$$