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

2023 India Regional Mathematical Olympiad, 1
Tags: number theory , RMO 2023 , Squares , Divisibility
Let $\mathbb{N}$ be the set of all positive integers and $S=\left\{(a, b, c, d) \in \mathbb{N}^4: a^2+b^2+c^2=d^2\right\}$. Find the largest positive integer $m$ such that $m$ divides abcd for all $(a, b, c, d) \in S$.

2023 India Regional Mathematical Olympiad, 6
Tags: Combo , combinatorics , RMO 2023
Consider a set of $16$ points arranged in $4 \times 4$ square grid formation. Prove that if any $7$ of these points are coloured blue, then there exists an isosceles right-angled triangle whose vertices are all blue.