What does $(a,b) = 1$ mean in the context of the irrationality of $\sqrt 2$?

Question

I was reading a proof for $\sqrt 2$ (which is a standard easy proof), but I came across a notation I've never seen. It says this:

If $ \sqrt 2$ is rational then the equation $$ a^2 = 2 b^2 $$ is soluble in integers $a,b$ with $(a,b) = 1$.

What does that mean?

soluble in integers $a,b$ with $(a,b) = 1$.

I am just unfamiliar with the notation. I am sure it's easy.

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All proof:

source: http://www.cs.kun.nl/~freek/notes/sketches.pdf

Answer 1

The expression "$a^2=2b^2$ is soluble in integers $a,b$ with $(a,b)=1$" is simply another way of saying that there exists a solution $(a,b)$ where $a,b\in\mathbb{Z}$ and $\gcd(a,b)=1$.