**Proposition**: Congruence Classes

Let $m> 0$ be a positive integer. The relation $”\equiv”$ of being congruent modulo $m$ is an equivalence relation $\equiv\subset\mathbb Z\times \mathbb Z,$ defined on the set of all integers $\mathbb Z.$ In particular, every element of the quotient set $[a]\in\mathbb Z_m$, written $a(m)$, is called the **congruence class modulo** $m$.

| | | | | created: 2019-04-10 21:08:18 | modified: 2019-04-11 07:34:24 | by: *bookofproofs* | references: [1272], [8152]

## 1.**Proof**: *(related to "Congruence Classes")*

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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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