INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A29 DISJUNCTIVE RADO NUMBERS FOR x1 + x2 + c = x3

Abstract

Given two equations E1 and E2, the disjunctive Rado number for E1 and E2 is the least integer n, provided that it exists, such that for every coloring of the set {1, 2,..., n} with two colors there exists a monochromatic solution to either E1 or E2. If no such integer n exists, then the disjunctive Rado number for E1 and E2 is infinite. Let R(c, k) represen