PreprintCC BY-NC-ND 4.0arXiv
An elementary proof of the 2-regularity of Pythagorean triples
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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BibTeX
@misc{wesley2026elementary,
title = {{An elementary proof of the 2-regularity of Pythagorean triples}},
author = {William J. Wesley},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39063},
eprint = {2609.39063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39063},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - An elementary proof of the 2-regularity of Pythagorean triples
AU - William J. Wesley
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39063
UR - https://arxiv.org/abs/2609.39063
AB - 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.
ER -