# Divisor of Integer/Examples

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## Examples of Divisors of Integers

### $2$ divides $4$

$2 \divides 4$

### $3$ divides $12$

$3 \divides 12$

### $4$ divides $\paren {-12}$

$4 \divides \paren {-12}$

### $2$ does not divide $5$

$2 \nmid 5$

### $3$ does not divide $4$

$3 \nmid 4$

### $3$ does not divide $10$

$3 \nmid 10$

### $2$ divides $n \paren {n + 1}$

Let $n$ be an integer.

Then:

$2 \divides n \paren {n + 1}$

### $3$ divides $n \paren {n + 1} \paren {n + 2}$

Let $n$ be an integer.

Then:

$3 \divides n \paren {n + 1} \paren {n + 2}$

### $6$ divides $n \paren {n + 1} \paren {n + 2}$

Let $n$ be an integer.

Then:

$6 \divides n \paren {n + 1} \paren {n + 2}$

### $6$ divides $7^n - 1$

Let $n \in \Z_{\ge 0}$ be a positive integer.

Then:

$6 \divides 7^n - 1$

where $\divides$ denotes divisibility.

### $63$ divides $8^{2 n} - 1$

Let $n \in \Z_{\ge 0}$ be a positive integer.

Then:

$63 \divides 8^{2 n} - 1$

where $\divides$ denotes divisibility.

### $80$ divides $9^{2 n} - 1$

Let $n \in \Z_{\ge 0}$ be a non-negative integer.

Then:

$80 \divides 9^{2 n} - 1$

where $\divides$ denotes divisibility.