Q:

Set of all $a\in\mathbb Z$ that are coprime to $b\in\mathbb Z$

$\newcommand\Z{\mathbb{Z}}$I'm looking for a standard or reasonable notation for
$$ \{a\in\Z : a\perp b\} = \{a\in\Z : \gcd(a,b)=1\} $$
My problem is that:

It is not $\Z/b\Z^*$, since for me, $1\neq b+1$.
It cannot be $\Z_b$, since that are the $b$-adic integers.

So I'm unable to find something fitting. It is not crucial (I can write it out every time), but it would be helpful. Any ideas?

A:

I suppose you could write this as
$$
\bigcup \left(\mathbb Z\big/b\mathbb Z\right)^*,
$$
where the union just throws the invertible cosets in $\mathbb Z\big/b\mathbb Z$ together.
Anyway, this isn't standard in any way, nor is it more comprehensible than defining some notation like
$$
\mathcal C_b = \{\,a\in\mathbb Z \mid \gcd(a,b)=1\,\}
$$
on your own. Where $\mathcal C$ is supposed to suggest coprime.
You could also just write "Let $a\in\mathbb Z$ with $(a,b)=1$", since $(a,b)$ is often used to denote $\gcd(a,b)$ in this context.

