Algebraic Structures, need help interpreting question

[bhoom]

Homework Statement

Prove that if gcd(a,b)=1 then N\ S(a,b) is a finite set.

Homework Equations

The Attempt at a Solution

I'm new to set theory and this question is from a voluntary course that dont give any credit.

I'm not sure how to start off here. What does the S(a,b) mean?
If it's the successor, then the proof is obvious? Any integers between 0 and a or b, will be the relative complement of N\S(a,b) and then finite...?

If S(a,b) is something else, what Is it? Perhaps the "ordered pair equivalence relation"?

I dont know any of either "ordered pair equivalence relation" or successor, I just compared what I read on wiki to the problem, and it looked like it could be relevant.
But if I can get some help to understand the problem I can read up on the relevant topics and then see what I can do to solve it.

 

[spamiam]

Just guessing from the context, and I don't think this is standard notation, but I think
$$S(a,b) = \{ma+nb: m, n \in \mathbb{N}\}$$
which is sort of like the idea of span from linear algebra. But you'd have to ask the professor to be sure.