Question 58
Let $n$ be a positive integer. A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is $n$-positive if all real numbers $x_{1}, \ldots, x_{n}$ satisfying $x_{1}+\ldots+x_{n}=0$ also satisfy $f\left(x_{1}\right)+\ldots+f\left(x_{n}\right) \geqslant 0$.
a) Is every 2020-positive function necessarily 1010-positive?
b) Is every 1010-positive function necessarily 2020-positive?
a) Is every 2020-positive function necessarily 1010-positive?
b) Is every 1010-positive function necessarily 2020-positive?