---- > [!definition] Definition. ([[congruent]]) > Given $n \in \mathbb{N}$ and $a,b \in \mathbb{Z}$, we say **$a$ is congruent to $b$ modulo $n$** and write $a \equiv b \text{ mod }n$ if $a \text{ mod } n = b \text{ mod }n,$ or equivalently if $n | (a-b)$. \ Congruence forms an [[equivalence relation]] on $\mathbb{Z}$, the [[equivalence class|equivalence classes]] of which are called **congruence classes**. ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```