Rado Numbers fora(x+y)=bz
In the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed that anyk-coloring of the numbers 1,2,…,Ncontains a monochromatic solution of a given system of linear equations. We will determine Rak(a,b) for the equationa(x+y)=bzifb=2 andb=a+1. Also, the case of monochr...
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| Veröffentlicht in: | Journal of combinatorial theory. Series A 1997-11, Vol.80 (2), p.356-363 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed that anyk-coloring of the numbers 1,2,…,Ncontains a monochromatic solution of a given system of linear equations. We will determine Rak(a,b) for the equationa(x+y)=bzifb=2 andb=a+1. Also, the case of monochromatic sequences {xn} generated bya(xn+xn+1)=bxn+2 is discussed. |
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| ISSN: | 0097-3165 1096-0899 |
| DOI: | 10.1006/jcta.1997.2810 |