Let $m> 0$ be a positive integer. The relation "$\equiv(m)$" of being congruent modulo $m$ is an equivalence relation $\equiv(m)\subset\mathbb Z\times \mathbb Z,$ defined on the set of all integers $\mathbb Z.$ In particular, every element $[a]$ of the quotient set, written $a(m)$, is called the congruence class modulo $m$. The quotient set $$\mathbb Z_m:=\mathbb Z/_{\equiv(m)}=\{0(m),1(m),\ldots,(m-1)(m)\}$$ contains the $m$ congruence classes modulo $m.$
Proofs: 1
Corollaries: 1
Definitions: 2 3 4
Explanations: 5
Lemmas: 6 7
Proofs: 8 9 10 11 12 13 14 15 16 17 18
Propositions: 19 20 21 22 23 24 25 26 27
Sections: 28 29
Theorems: 30 31
