Question 1
Let $\mathbb Z$ be the set of integers. Determine all functions $f:\mathbb Z\to\mathbb Z$ such that, for all integers $a,b$,
$$f(2a)+2f(b)=f(f(a+b)).$$
$$f(2a)+2f(b)=f(f(a+b)).$$
IMO · International Mathematical Olympiad 2019 — Official contest