Number Theory | No Common Factor Notation?

Question

I have a question about notation in number theory:

Is there a notation for a set of integers to not have a common factor?

Maybe something like: $\neg\exists\, gcd(\{z \in \mathbb{Z}\,|\,whatever\})$?

Edit: where $gcd(my set) \not=1$

I'm looking for notation for writing a proof that $\sqrt{3} \notin \mathbb{Q} \,$ (i.e, it's irrational).

*Note: I didn't learn number theory. This proof I want to do is an exercise from a preparation lesson to calculus (about axioms of $\mathbb{R}$eal numbers and a few other things).

Thanks a lot to the helpers in advance! :D

Answer 1

let $$a,b$$ are integer numbers, then we can write GCD(a,b)=1