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2023 RMO

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Contents

1 Problem 1
2 Problem 2
3 Problem 3
4 Problem 4
5 Problem 5
6 Problem 6

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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