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==Solution==
Marijn Heule, Oliver Kullmann, and Victor W. Marek demonstrated that it is possible to partition the set <math>\{1, \ldots, 7824\}</math> into two subsets such that neither subset contains a Pythagorean triple. However, such a partition is not possible for the set <math>\{1, \ldots, 7825\}</math>. This result was achieved by analyzing a vast number of possible colorings, which initially amounted to about <math>2^{7825}</math> combinations. The researchers reduced this to around a trillion cases, which were then tested using a SAT solver. The computational process required approximately 4 CPU-years over two days on the Stampede supercomputer at the Texas Advanced Computing Center. The resulting proof, initially 200 terabytes in size, was compressed to 68 gigabytes.The findings were published in the SAT 2016 conference paper "Solving and Verifying the Boolean Pythagorean Triples problem via Cube-and-Conquer," which received the best paper award.
==Prize==
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