The problem: Let a,b be coprime positive integers. Prove that for any integer n there exists s,t with s>0 such that sa+ tb=n.

My work so far (do not know if I am on the right path):

If a,b are coprime there exists s,t in the integers that sa+tb=1.

This is by definition that is given in our text.

Since, in addition, a,b are positive integers then there are two possible scenarios for s,t as follows:

1. s>0 and t<0

2.s<0 and t>0

This problem has given me a headache

I will greatly appreciate your feedback!

Thanks!