English

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 rr-coloring of a set SS is a surjective function c:S[r]c:S\to [r]. The rainbow number of a set SS for equation eqeq is the smallest integer rr such that every exact rr-coloring of SS contains a rainbow solution to eqeq. In this paper, the rainbow number of Zp\Z_p, for pp prime and the equation a1x1+a2x2+a3x3=ba_1x_1 + a_2x_2 + a_3x_3 = b is determined. The rainbow number of Zn\Z_{n}, for a natural number nn, is determined under certain conditions.

Keywords

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}
}