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An exact $r$-coloring of a set $S$ is a surjective function $c:S\to [r]$. Therainbow number of a set $S$ for equation $eq$ is the smallest integer $r$ suchthat every exact $r$-coloring of $S$ contains a rainbow solution to $eq$. Inthis 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.

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