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: 2

1995 Miklós Schweitzer, 5
Tags: additive combinatorics , fourier analysis , combinatorics
Let A be a subset of the set $\{1,2, ...,n\}$ with at least $100\sqrt n$ elements. Prove that there is a four-element arithmetic sequence in which each element is the sum of two different elements of the set A.

2021 Miklós Schweitzer, 6
Tags: real analysis , fourier analysis
Let $f$ and $g$ be $2 \pi$-periodic integrable functions such that in some neighborhood of $0$, $g(x) = f(ax)$ with some $a \neq 0$. Prove that the Fourier series of $f$ and $g$ are simultaneously convergent or divergent at $0$.