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arXiv · 2609.39063

An elementary proof of the 2-regularity of Pythagorean triples

William J. Wesley
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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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William J. Wesley. 2026-09-30. An elementary proof of the 2-regularity of Pythagorean triples. https://arxiv.org/abs/2609.39063

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