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

Tags were heavily modified to better represent problems.

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Found problems: 2

2022 Mexico National Olympiad, 1
Tags: primes , reciprocals
A number $x$ is "Tlahuica" if there exist prime numbers $p_1,\ p_2,\ \dots,\ p_k$ such that \[x=\frac{1}{p_1}+\frac{1}{p_2}+\dots+\frac{1}{p_k}.\] Find the largest Tlahuica number $x$ such that $0<x<1$ and there exists a positive integer $m\leq 2022$ such that $mx$ is an integer.

2024 Bulgaria National Olympiad, 3
Tags: algebra , functional equation , reciprocals , bijectivity
Find all functions $f:\mathbb {R}^{+} \rightarrow \mathbb{R}^{+}$, such that $$f(af(b)+a)(f(bf(a))+a)=1$$ for any positive reals $a, b$.