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 $m.$

| | | | | created: 2019-04-10 21:08:18 | modified: 2019-06-20 08:26:14 | by: *bookofproofs* | references: [1272], [8152]

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[8152] **Jones G., Jones M.**: “Elementary Number Theory (Undergraduate Series)”, Springer, 1998

[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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