The 2-color Rado Number of x1+x2+·s +xm-1=axm, II
Abstract
In the first installment of this series, we proved that, for every integer a≥ 3 and every m≥ 2a2-a+2, the 2-color Rado number of x1 + x2 + ·s + xm-1 = axm is m-1a m-1a . Here we obtain the best possible improvement of the bound on m. We prove that if 3|a then the 2-color Rado number is m-1a m-1a when m≥ 2a+1 but not when m=2a, and that if 3 a then the 2-color Rado number is m-1a m-1a when m≥ 2a+2 but not when m=2a+1. We also determine the 2-color Rado number for all a≥ 3 and m≥ a2+1.
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