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A van der Waerden-free proof of Rado’s theorem
Mauro Di Nasso, Lorenzo Luperi Baglini
Source 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”.
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