MathDB

Let p be an odd prime, A be a non-empty subset of residue classes modulo p,

f:A\to\mathbb R

. Suppose that f is not constant and satisfies

f(x) \leq \frac{f(x + h) + f(x-h)}{2}

whenever

x,x+h,x-h\in A

. Prove that

|A| \leq \frac{p + 1}{2}

Problem Statement