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 monochromatic sequences {xn} generated bya(xn+xn+1)=bxn+2 is discussed.