Common Divisor in Integral Domain Divides Linear Combination

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

That is:
 * $$a, b, c \in \Z: c \backslash a \and c \backslash b$$.

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


 * $$\forall p, q \in \Z: c \backslash \left({p a + q b}\right)$$

Proof
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