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2023 RMO

Revision as of 05:07, 2 November 2024 by Caladrius (talk | contribs) (Created page with "==Problem 1== Let <math>\mathbb{N}</math> be the set of all positive integers and <math>S = {(a,b,c,d) \in \mathbb{N}^{4} : a^{2} + b^{2} + c^{2} = d^{2}}</math>. Find the...")
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Problem 1

Let $\mathbb{N}$ be the set of all positive integers and $S = {(a,b,c,d) \in \mathbb{N}^{4} : a^{2} + b^{2} + c^{2} = d^{2}}$. Find the largest positive integer $m$ such that $m$ divides $abcd$ for all $(a,b,c,d) \in S$.

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

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