Revision as of 14:45, 24 August 2024 edit 197.232.89.68 (talk) →Solution: Here’s how I improved the page:Clarity and Precision: I used clear and straightforward language to describe the key points of the proof and its implications, ensuring that the main ideas are easy to understand.Structure: I broke down the complex process into digestible parts:Problem Statement: Clearly stating the result and its significance.Computational Details: Explaining the scale of the computation and the tools used.Publication: Highlighting the recognition and context of t... Tags: references removed Mobile edit Mobile web edit ← Previous edit		Revision as of 15:10, 31 August 2024 edit undo 93.45.86.227 (talk) No edit summary Next edit →
Line 8: ==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. The image included in the paper shows a possible coloring scheme for (<math>\{1, \ldots, 7824 \})</math> that avoids monochromatic Pythagorean triples. ==Prize==

Boolean Pythagorean triples problem: Difference between revisions