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Given two equations E 1 and E 2 , the disjunctive Rado number for E 1 and E 2 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 E 1 or E 2. If no such integer n exists, then the disjunctive Rado number for E 1 and E 2 is infinite. Let R(c,(More)
For integers n ≥ 1 and k ≥ 0, let M k (n) represent the minimum number of monochromatic solutions to x + y < z over all 2-colorings of {k + 1, k + 2,. .. , k + n}. We show that for any k ≥ 0, M k (n) = Cn 3 (1 + o k (1)), where C = 1 12(1+2 √ 2) 2 ≈ .005686. A structural result is also proven, which can be used to determine the exact value of M k (n) for(More)
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