This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

1999 IMC, 6
Tags: fourier series , complex number , pigeonhole principle
Let $A$ be a subset of $\mathbb{Z}/n\mathbb{Z}$ with at most $\frac{\ln(n)}{100}$ elements. Define $f(r)=\sum_{s\in A} e^{\dfrac{2 \pi i r s}{n}}$. Show that for some $r \ne 0$ we have $|f(r)| \geq \frac{|A|}{2}$.