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Rado Numbers fora(x+y)=bz

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Publication Date
Volume
80
Issue
2
Identifiers
DOI: 10.1006/jcta.1997.2810

Abstract

Abstract In the case of existence the smallest number N=Ra k is called a Rado number if it is guaranteed that any k-coloring of the numbers 1, 2, …, Ncontains a monochromatic solution of a given system of linear equations. We will determine Ra k ( a, b) for the equation a( x+ y)= bzif b=2 and b= a+1. Also, the case of monochromatic sequences { x n } generated by a( x n + x n+1 )= bx n+2 is discussed.

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