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Preprint Number 1052

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1052. Mauro Di Nasso, Lorenzo Luperi Baglini
Ramsey properties of nonlinear Diophantine equations

Submission date: 7 June 2016


We prove general sufficient and necessary conditions for the partition regularity of Diophantine equations, which extend the classic Rado's Theorem by covering large classes of nonlinear equations. Sufficient conditions are obtained by exploiting algebraic properties in the space of ultrafilters βN, grounding on combinatorial properties of positive density sets and IP sets. Necessary conditions are proved by a new technique in nonstandard analysis, based on the use of the relation of u-equivalence for the hypernatural numbers *N.

Mathematics Subject Classification: 05D10, 11D99, 11U10

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Full text arXiv 1606.02056: pdf, ps.

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