> [!NOTE] Definition (Congruence Class) > The [[Equivalence relations|equivalence class]] of an integer $x$ under [[Congruence Modulo n|congruence modulo n]] is known as its *congruence* (or *residue*) class denoted $[x]_{n} = \{ y\in \mathbb{Z} : n \mid (x-y) \}$ # Properties **Operations**: We can define [[Modular arithmetic|addition & multiplication]] on congruence classes. These operations satisfy the required properties so that $(\mathbb{Z}/n\mathbb{Z},+,\times)$ is a *ring* where $\mathbb{Z}/n\mathbb{Z}$ is [[Integers modulo n|set of congruence classes modulo n]].