Boolean Pythagorean triples problem: Difference between revisions

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The '''Boolean Pythagorean triples problem''' was a [[Conjecture|conjecture]] relating to [[Pythagorean triple]]s which was shown to be false using a [[computer-assisted proof]] in May 2016.<ref>{{Cite journal|last=Lamb|first=Evelyn|date=26 May 2016|title=Two-hundred-terabyte maths proof is largest ever|url=http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-1.19990|journal=Nature|doi=10.1038/nature.2016.19990}}</ref>

This problem is part of the [[Infinitary_combinatoricsInfinitary combinatorics|Ramsey theory]] and asks if it is possible to color all the integers either red or blue so that no Pythagorean triple of integers ''a'', ''b'', ''c'', satisfying <math>a^2+b^2=c^2</math> are all the same color. For example if you would color ''a'' and ''b'' red, and ''c'' blue, this would successfully not satisfy the tested triple, but all triples would have to be tested.

The proof found out that up to the number 7,824 it is possible to color the numbers in such a way and that 10^2,300 colorings exist, but that for numbers above 7,825 no solutions exist. This means that for the problem question, we can say that no solution exists. The proof took two days of computer execution time on the Stampede supercomputer at the [[Texas Advanced Computing Center]] and generated 200 terabytes of data.