Simplify $[14]_8 \oplus[12]_8\oplus[31]_8$, where $[\cdot]$ denotes a residue class mod 8

Question

Simplify the following: $$[14]_8 \oplus[12]_8\oplus[31]_8$$

I have the following: \begin{align}&[14]_8 \oplus[12]_8\oplus[31]_8 \\ &=[14+12+31]_8 \\&=[57]_8 \\&=[57 + 8k \ | k \in \mathbb{Z}] \\&=[1]_8\end{align}

Is this correct?

Answer 1

This works. Addition and multiplication both "play nicely" in modular arithmetic.