Proving at most one affine permutation mapping $x$ to $u$ and $y$ to $v$ with $x,y \in \mathbb{Z}_n$ and $\gcd(x−y,n) = 1$

Suppose that $$x,y \in \mathbb{Z}_n$$ with $$\gcd(x−y,n) = 1$$. Prove that for any $$u,v \in \mathbb{Z}_n$$ there is at most one affine permutation mapping $$x$$ to $$u$$ and $$y$$ to $$v$$.

• Welcome to Cryptography. This is clearly a dump of homework. Where you stuck? – kelalaka Mar 31 at 9:56
• start with the definition of a permutation. – kodlu Apr 1 at 23:04