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arXiv · 2511.14660

A Van der Waerden-free proof of Rado's theorem

Mauro Di Nasso·Lorenzo Luperi Baglini
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Abstract

We present a proof of the sufficiency of Rado's condition for the partition regularity of linear Diophantine equations that avoids any use of van der Waerden's theorem. The proof is based on fundamental properties that are common knowledge in combinatorics of numbers and is entirely elementary, with the sole exception of a standard application of the compactness principle.

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Mauro Di Nasso, Lorenzo Luperi Baglini. 2026-08-11. A Van der Waerden-free proof of Rado's theorem. https://arxiv.org/abs/2511.14660

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