Divisor of Integer/Examples

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 $10$

$3 \nmid 10$

Divisors of $6$

The divisors of $6$ are $1$, $2$, $3$ and $6$.

$2$ 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.