# 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}
}```
• Published in SAT 3 May 2016
• Mathematics
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…
164 Citations
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