Abstract
Formulas for two-color Rado numbers have been established for many families of linear equations. However, there are no explicit formulas for two-color Rado numbers for any nonlinear equations. In this paper, we will establish formulas for the two-color Rado numbers for three families of equations: x + y n = z, x + y 2 + c = z, and x + y 2 = az , where c and a are positive integers.
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