**Definition**: Congruent, Residue

Let $m > 0$ be a positive integer. $a$ is called **congruent** to $b$ (or $a$ is called a **residue** of $b$) **modulo** $m$, written $$a\equiv b \mod m$$

or shorter

$$a\equiv b (m),$$

if $m\mid a-b,$ i.e. if $m$ is a divisor of the difference $a-b.$

| | | | | created: 2019-04-10 20:21:58 | modified: 2019-04-10 20:57:10 | by: *bookofproofs* | references: [1272], [8152]

(none)

[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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