Home > Algebra, Higher Algebra, Problem Solving > IMC 2010 Day 2 Problem 5

## IMC 2010 Day 2 Problem 5

Suppose that for a function $f:\Bbb{R}\to \Bbb{R}$ and real numbers $a one has $f(x)=0$ for all $x \in (a,b)$. Prove that $f(x)=0$ for all $x \in \Bbb{R}$ if
$\displaystyle \sum_{k=0}^{p-1}f\left( y+\frac{k}{p}\right)=0$ for every prime number $p$ and for every real number $y$.
IMC 2010 Day 2 Problem 5