Question 93
Let $f : [0, \infty) \to \mathbb{R}$ be a continuous function which is constant on the set of nonnegative integers. Suppose that for any real numbers $0 \le a \lt b \lt c \lt d$, such that $f(a) = f(c)$ and $f(b) = f(d)$, we have $f(\frac{a+b}{2}) = f(\frac{c+d}{2})$. Prove that $f$ is a constant function.
Florin Stănescu
Florin Stănescu