Difference between revisions of "2023 RMO"

(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...")
 
(Problem 6)
 
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==Problem 1==
 
==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 largest positive integer <math>m</math> such that <math>m</math> divides <math>abcd</math> for all <math>(a,b,c,d)  \in S</math>.
 
  
 
==Problem 2==
 
==Problem 2==

Latest revision as of 13:30, 9 December 2024

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6