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The '''Boolean Pythagorean triples problem''' is a problem relating to [[Pythagorean triple]]s which was solved using a [[computer-assisted proof]] in May 2016.<ref name="nature">{{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 from [[Ramsey theory]] and asks if it is possible to color each of the positive 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, in the Pythagorean triple 3, 4 and 5 (<math>3^2+4^2=5^2</math>), if 3 and 4 are colored red, then 5 must be colored blue.
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The paper describing the proof was published on arXiv on 3 May 2016,<ref name="arXiv">{{Cite arXiv|last=Heule|first=Marijn J. H.|last2=Kullmann|first2=Oliver|last3=Marek|first3=Victor W.|date=2016-05-03|title=Solving and Verifying the Boolean Pythagorean Triples problem via Cube-and-Conquer |arxiv=1605.00723 }}</ref> and has been accepted for the SAT 2016 conference, where it won the best paper award.<ref>[http://sat2016.labri.fr/ SAT 2016]</ref>
In the 1980s [[Ronald Graham]] offered a $100 prize for the solution of the problem, which has now been awarded to Marijn Heule.<ref
== References ==
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