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arXiv · 1905.06296

Rainbow Numbers of $\mathbb{Z}_n$ for $a_1x_1+a_2x_2+a_3x_3 =b$

Katie Ansaldi·Houssein El Turkey·Jessica Hamm·Anisah Nu'Man·Nathan Warnberg·Michael Young
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Abstract

An exact $r$-coloring of a set $S$ is a surjective function $c:S\to [r]$. The rainbow number of a set $S$ for equation $eq$ is the smallest integer $r$ such that every exact $r$-coloring of $S$ contains a rainbow solution to $eq$. In this paper, the rainbow number of $\Z_p$, for $p$ prime and the equation $a_1x_1 + a_2x_2 + a_3x_3 = b$ is determined. The rainbow number of $\Z_{n}$, for a natural number $n$, is determined under certain conditions.

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Katie Ansaldi, Houssein El Turkey, Jessica Hamm, Anisah Nu'Man, Nathan Warnberg, Michael Young. 2019-11-24. Rainbow Numbers of $\mathbb{Z}_n$ for $a_1x_1+a_2x_2+a_3x_3 =b$. https://arxiv.org/abs/1905.06296

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