One is Common Divisor of Integers

Theorem

Let $a, b \in \Z$ be integers.

Then $1$ is a common divisor of $a$ and $b$.

Proof

From One Divides all Integers:

$1 \divides a$

and:

$1 \divides b$

where $\divides$ denotes divisibility.

The result follows by definition of common divisor.

$\blacksquare$

Sources

• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor