Exactly one solution to $ x\cdot a +y\cdot b = c $ with given $a,b \in \mathbb{N}\; c \in \mathbb{Z}$

Question

how do I show that

$ x\cdot a +y\cdot b = c $

with $a,b \in \mathbb{N}$ and $c \in \mathbb{Z}$

has exactly one solution in $\mathbb{Z}$.

(There are 2 numbers $u,v \in \mathbb{Z}$ with $ua+vb = c$)

if

$gcd(a,b)\mid c$

I have no idea how to start the proof.

Any help is greatly appreciated.