On Generalized Schur Numbers of the Equation x+ay=z

On Generalized Schur Numbers of the Equation x+ay=z

Let a and r be positive integers. By definition, sar is the least positive integer such that, for any r-coloring of the interval 1,sar, there exists a monochromatic solution to x+ay=z. For a=1, the numbers sr=s1r are classical Schur numbers. In this paper, we study the numbers sar for a≥2.

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Veröffentlicht in:Journal of Mathematics 2020, Vol.2020 (2020), p.1-5
1. Verfasser: Khamseh, Amir
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Schur, Issai
Theory
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Zusammenfassung:Let a and r be positive integers. By definition, sar is the least positive integer such that, for any r-coloring of the interval 1,sar, there exists a monochromatic solution to x+ay=z. For a=1, the numbers sr=s1r are classical Schur numbers. In this paper, we study the numbers sar for a≥2.
ISSN:2314-4629
2314-4785
DOI:10.1155/2020/7069730