Affiliation:
1. Department of Mathematics, Kharazmi University, 15719-14911 Tehran, Iran
Abstract
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.