2019 IMO Shortlist A1

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

令 $\mathbb{Z}$ 为整数集。确定所有函数 $f: \mathbb{Z} \rightarrow \mathbb{Z}$，使得对于所有整数 $a$ 和 $b$，$$f(2 a)+2 f(b)=f(f(a+b))$$ (南非)