We present a proof of the sufficiency of Rado’s condition for the partition regularity of linear Diophantine equations that avoids any use of vander Waerden’s theorem. The proof is based on fundamental properties that are common knowledge in combinatorics of numbers and is entirely “elementary”.
A van der Waerden-free proof of Rado’s theorem / M. Di Nasso, L.L.B.. - In: COMPTES RENDUS MATHÉMATIQUE. - ISSN 1631-073X. - 364:G3(2026 Oct), pp. 605-615. [10.5802/crmath.852]
A van der Waerden-free proof of Rado’s theorem
L. Luperi Baglini
Ultimo
2026
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 vander Waerden’s theorem. The proof is based on fundamental properties that are common knowledge in combinatorics of numbers and is entirely “elementary”.
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