Notation question, parentheses

Question

Hi this is simple question, but it's been troubling me for some time because I can't find anywhere what does it actually mean (algebra) -

$(a,b)=1$

is it GCD of those two values?

Answer 1

Yes, that means that $\operatorname{gcd}(a,b) = 1$, that the greatest common divisor among $a$ and $b$ is one. That is, that the numbers are coprime, or relatively prime.

The notation $a \perp b$ is also used to denote $\operatorname{gcd}(a,b) = 1$.

Answer 2

The notation is commonly usd for the gcd, but it can also mean the ideal generated by $a$ and $b$.

That these notations clash has some sense as under certain conditions the ideal generated by $a$ and $b$ is just the ideal generated by a gcd of $a$ and $b$.

Answer 3

It means that $a$ and $b$ are coprime, that their greatest common divisor (GCD) is $1$. But it's much better to write $\gcd(a, b) = 1$; if you're printing the paper out, what you lose in ink you gain in clarity.