Rainbow Numbers of $\mathbb{Z}_n$ for $a_1x_1+a_2x_2+a_3x_3 =b$
Combinatorics
2019-11-26 v2
Abstract
An exact -coloring of a set is a surjective function . The rainbow number of a set for equation is the smallest integer such that every exact -coloring of contains a rainbow solution to . In this paper, the rainbow number of , for prime and the equation is determined. The rainbow number of , for a natural number , is determined under certain conditions.
Cite
@article{arxiv.1905.06296,
title = {Rainbow Numbers of $\mathbb{Z}_n$ for $a_1x_1+a_2x_2+a_3x_3 =b$},
author = {Katie Ansaldi and Houssein El Turkey and Jessica Hamm and Anisah Nu'Man and Nathan Warnberg and Michael Young},
journal= {arXiv preprint arXiv:1905.06296},
year = {2019}
}