Can one split the integers into two sets such that every Pythagorean triple spans both?
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members. The Boolean Pythagorean triples problem was solved by Marijn Heule, Oliver Kullmann and Victor W. Marek in May 2016 through a computer-assisted proof.[1]
^Lamb, Evelyn (26 May 2016). "Two-hundred-terabyte maths proof is largest ever". Nature. 534 (7605): 17–18. Bibcode:2016Natur.534...17L. doi:10.1038/nature.2016.19990. PMID 27251254.
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Primitive Pythagoreantriples have been used in cryptography as random sequences and for the generation of keys. BooleanPythagoreantriplesproblem Congruum...
Solver Competition. Cube-and-Conquer was used to solve the BooleanPythagoreantriplesproblem. Cube-and-Conquer is a modification or a generalization of...
Oliver; Marek, Victor W. (2016). "Solving and Verifying the BooleanPythagoreanTriplesProblem via Cube-and-Conquer". Theory and Applications of Satisfiability...
Lee, 2017) BooleanPythagoreantriplesproblem (Marijn Heule, Oliver Kullmann, Victor W. Marek, 2016) Sensitivity conjecture for Boolean functions (Hao...
the BooleanPythagoreantriplesproblem required the generation of 200 terabytes of proof. 2017 Marijn Heule, who coauthored solution to the Boolean Pythagorean...
hulls. He also began the study of primefree sequences, the BooleanPythagoreantriplesproblem, the biggest little polygon, and square packing in a square...
solvers to resolve mathematical conjectures such as the BooleanPythagoreantriplesproblem, Schur's theorem number 5, and Keller's conjecture in dimension...
Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagoreantriples. It was originally written in the Polish language...
numbers 1 through n such that every Pythagoreantriple is multicolored, i.e. where the BooleanPythagoreantriplesproblem becomes false. The 200-terabyte...
classification of finite simple groups. The Kepler conjecture. The BooleanPythagoreantriplesproblem. British Museum algorithm Computer-assisted proof Enumerative...
1890 BC). All of these texts mention the so-called Pythagoreantriples, so, by inference, the Pythagorean theorem seems to be the most ancient and widespread...
subject of Pythagoreantriples, even if it had been well understood may still not have featured in the Sulvasutras. The occurrence of the triples in the Sulvasutras...
from 2000 to 1800 BC. Many early texts mention Pythagoreantriples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread...
Plimpton 322 Babylonian tablet records the oldest known examples of Pythagoreantriples. 1800 BC – Egypt, Moscow Mathematical Papyrus, finding the volume...
Vija-Ganita, which contain problems dealing with determinate and indeterminate linear and quadratic equations, and Pythagoreantriples and he fails to distinguish...
equations, in the form of problems relating the areas and sides of rectangles, are solved by Babylonians. 2000 BC: Pythagoreantriples are first discussed in...
[citation needed] c. 1800 BC The Plimpton 322 tablet gives a table of Pythagoreantriples in Babylonian Cuneiform script. 1800 BC Berlin Papyrus 6619 (19th...
IEEE Transactions. C (21): 1197–1206. Church, A. (1936). "An unsolvable problem of elementary number theory (first presented on 19 April 1935 to the American...
nanotechnology Theano (6th century BC), one or possibly two different Pythagorean philosophers Diana Thomas, American mathematician who studies nutrition...
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