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

2017 Iran MO (3rd round), 1
Let $x$ and $y$ be integers and let $p$ be a prime number. Suppose that there exist realatively prime positive integers $m$ and $n$ such that $$x^m \equiv y^n \pmod p$$ Prove that there exists an unique integer $z$ modulo $p$ such that $$x \equiv z^n \pmod p \quad \text{and} \quad y \equiv z^m \pmod p$$
iran 3rd round order bezout Bézout's identity modular arithmetic number theory

2024 Iran MO (3rd Round), 2
A surjective function $g: \mathbb{C} \to \mathbb C$ is given. Find all functions $f: \mathbb{C} \to \mathbb C$ such that for all $x,y\in \mathbb C$ we have $$ |f(x)+g(y)| = | f(y) + g(x)|. $$ Proposed by [i]Mojtaba Zare, Amirabbas Mohammadi[/i]
iran 3rd round functional equation algebra complex number casework complex numbers functional equations