Modulo Addition/Cayley Table/Modulo 5

Cayley Table for Modulo Addition
The additive group of integers modulo $m$ can be described by showing its Cayley table.

This one is for modulo $5$:


 * $\begin{array} {r|rrrrr}

\struct {\Z_5, +_5} & \eqclass 0 5 & \eqclass 1 5 & \eqclass 2 5 & \eqclass 3 5 & \eqclass 4 5 \\ \hline \eqclass 0 5 & \eqclass 0 5 & \eqclass 1 5 & \eqclass 2 5 & \eqclass 3 5 & \eqclass 4 5 \\ \eqclass 1 5 & \eqclass 1 5 & \eqclass 2 5 & \eqclass 3 5 & \eqclass 4 5 & \eqclass 0 5 \\ \eqclass 2 5 & \eqclass 2 5 & \eqclass 3 5 & \eqclass 4 5 & \eqclass 0 5 & \eqclass 1 5 \\ \eqclass 3 5 & \eqclass 3 5 & \eqclass 4 5 & \eqclass 0 5 & \eqclass 1 5 & \eqclass 2 5 \\ \eqclass 4 5 & \eqclass 4 5 & \eqclass 0 5 & \eqclass 1 5 & \eqclass 2 5 & \eqclass 3 5 \\ \end{array}$

which can also be presented:


 * $\begin{array} {r|rrrrr}

+_5 & 0 & 1 & 2 & 3 & 4 \\ \hline 0 & 0 & 1 & 2 & 3 & 4 \\ 1 & 1 & 2 & 3 & 4 & 0 \\ 2 & 2 & 3 & 4 & 0 & 1 \\ 3 & 3 & 4 & 0 & 1 & 2 \\ 4 & 4 & 0 & 1 & 2 & 3 \\ \end{array}$