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: 2019-07-28 09:28:53 | by: bookofproofs | references: [1272], [8152]

1.Proposition: Congruence Classes 

2.Proposition: Congruences and Division with Quotient and Remainder 

3.Explanation: Explanation of Congruence Classes 

4.Proposition: Connection between Quotient, Remainder, Modulo and Floor Function 

5.Lemma: Coprimality and Congruence Classes 

6.Proposition: Multiplication of Congruences with a Positive Factor 

7.Proposition: Congruence Modulo a Divisor 

8.Definition: Modulo Operation for Real Numbers