#### Document Type

Thesis - Open Access

#### Award Date

2022

#### Degree Name

Master of Science (MS)

#### Department / School

Mathematics and Statistics

#### Abstract

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).

#### Library of Congress Subject Headings

Ramsey theory.

Combinatorial analysis.

Rado numbers

#### Number of Pages

32

#### Publisher

South Dakota State University

#### Recommended Citation

Halverson, Skylar, "Totally Multicolored Rado Numbers For the Equation x_1 + x_2 + x_3 + ... + x_(m−1) = x_m" (2022). *Electronic Theses and Dissertations*. 399.

https://openprairie.sdstate.edu/etd2/399