The Boolean Pythagorean triples problem asks whether the positive integers can be colored in two colors, red and blue, so that no Pythagorean triple has all three of its members the same color. It belongs to Ramsey theory, the branch of combinatorics that studies how much order must survive any attempt to split a set into pieces. Marijn Heule, Oliver Kullmann and Victor Marek settled the problem in May 2016 with a computer-assisted proof, showing that such a two-coloring exists only up to the number 7,824 and can't be extended any further than that.
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StatementCan the positive integers be colored red and blue so that no Pythagorean triple a, b, c with a^2 + b^2 = c^2 has all three members the same color? The answer is that such a coloring exists only up to the number 7824. 1 Classification
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Source Boolean Pythagorean triples problem, Wikipedia
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1. Boolean Pythagorean triples problem, Wikipedia
Lead paragraph, first sentence
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members.
Lead paragraph, second sentence
The Boolean Pythagorean triples problem was solved by Marijn Heule, Oliver Kullmann and Victor W. Marek in May 2016 through a computer-assisted proof, which showed that such a coloring is only possible up to the number 7824.
Lead paragraph
The Boolean Pythagorean triples problem was solved by Marijn Heule, Oliver Kullmann and Victor W. Marek in May 2016 through a computer-assisted proof
In Group: Ramsey Theory and Extremal Combinatorics, Lead section
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored
In Branch: Combinatorics, Lead section
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored
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