I'm not quite sure how to start on this problem.

Let be mutually prime where .

Let be any integers,then there exists x such that .

Suppose .

Suppose has a solution mod for .

Prove that has a solution mod n.

I don't need to find the solution, just show that one exists.

Do I use the actual solution of , or just the fact that it has a solution. Sorry, I'm just lost on this problem.