All two-color Rado numbers for a(x + y) = bz Original Research Article

If it exists, the smallest number N = Rk(∑) is called the kth Rado number of a given system ∑ of linear equations if it is guaranteed that any k-coloring of the numbers 1, 2, …, N contains a monochromatic solution of ∑. For the family of equations a(x + y) = bz, all Rado numbers R2(a,b) are determined. © 1999 Elsevier Science B.V. All rights reserved