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...") |
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==Problem 6== | ==Problem 6== | ||
| + | Consider a set of <math>16</math> points arranged in a <math>4\times4</math> square grid formation. Prove that if any <math>7</math> of these points are coloured blue, then there exists an isosceles right-angled triangle whose vertices are all blue. | ||
Revision as of 07:51, 2 November 2024
Problem 1
Let 
be the set of all positive integers and 
. Find the largest positive integer 
such that divides 
for all 
.
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Consider a set of 
points arranged in a 
square grid formation. Prove that if any 
of these points are coloured blue, then there exists an isosceles right-angled triangle whose vertices are all blue.
