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An elementary proof of the 2-regularity of Pythagorean triples
William J. Wesley
Source abstract
We give a new proof of the fact that every 2-coloring of the positive integers contains a monochromatic Pythagorean triple. This result was originally proven by Heule, Kullmann, and Marek with SAT solvers in 2016, answering a decades-old question of Graham. This proof uses elementary techniques and requires neither lengthy computation nor difficult analytic machinery.
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