Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer

@inproceedings{Heule2016SolvingAV,
  title={Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer},
  author={Marijn J. H. Heule and Oliver Kullmann and Victor W. Marek},
  booktitle={SAT},
  year={2016}
}
The boolean Pythagorean Triples problem has been a longstanding open problem in Ramsey Theory: Can the set N = $\{1, 2, ...\}$ of natural numbers be divided into two parts, such that no part contains a triple $(a,b,c)$ with $a^2 + b^2 = c^2$ ? A prize for the solution was offered by Ronald Graham over two decades ago. We solve this problem, proving in fact the impossibility, by using the Cube-and-Conquer paradigm, a hybrid SAT method for hard problems, employing both look-ahead and CDCL… 
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