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For every integer m ≥ 3 and every integer c, let r m c be the least integer, if it exists, such that for every 2-coloring of the set 1 2 r m c there exists a monochromatic solution to the equation

If L 1 and L 2 are linear equations, then the disjunctive Rado number of the set {L 1 , L 2 } is the least integer n, provided that it exists, such that for every 2-coloring of the set {1, 2, . . . , n} there exists a monochromatic solution to either L 1 or L 2 . If such an integer n does not exist, then the disjunctive Rado number is infinite. In this paper, it is shown that for all integers a 1 and b 1, the disjunctive Rado number for the equations x 1 + a = x 2 andgcd(a,b) is odd and the disjunctive Rado number for these equations is infinite otherwise. It is also shown that for all integers a > 1 and b > 1, the disjunctive Rado number for the equations ax 1 = x 2 and bx 1 = x 2 is c s+t−1 if there exist natural numbers c, s, and t such that a = c s and b = c t and s + t is an odd integer and c is the largest such integer, and the disjunctive Rado number for these equations is infinite otherwise.

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