Totally Multicolored Rado Numbers For the Equation x_1 + x_2 + x_3 + ... + x_(m−1) = x_m

A set is called Totally Multicolored (TMC) if no elements in the set are colored the same. For all natural numbers t, m, let R(t, m) be the least natural number n such that for every t-coloring of the set {1, 2, 3, ..., R(t, m)} there exist a solution set {x_1, x_2, . . ., x_m} to L(m), x_1 + x_2 + x_3 + ... + x_(m−1) = x_m such that x_i does not equal x_j for all i that does not equal j, that avoids being Totally Multicolored. This paper shows a function to find R(t,m) for any t greater than or equal to 1 and m greater than or equal to 3. See the abstract in the text for the function that gives R(t,m)