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<b 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

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