# Common Divisor Divides Integer Combination/Proof 1

## Corollary to Common Divisor in Integral Domain Divides Linear Combination

Let $c$ be a common divisor of two integers $a$ and $b$.

That is:

$a, b, c \in \Z: c \divides a \land c \divides b$

Then $c$ divides any integer combination of $a$ and $b$:

$\forall p, q \in \Z: c \divides \paren {p a + q b}$

## Proof

We have that the Integers form Integral Domain.

The result then follows from Common Divisor in Integral Domain Divides Linear Combination.

$\blacksquare$