Symbols:Z

The Set of Integers
$$\mathbb{Z}$$

The set of integers: $$\mathbb{Z} = \left\{{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}\right\}$$.

From the German "Zahlen", which means "(whole) numbers".

Its LaTeX code is \mathbb{Z}.

The Set of Non-Zero Integers
$$\mathbb{Z}^*$$

The set of non-zero integers: $$\mathbb{Z}^* = \left\{{\ldots, -3, -2, -1, 1, 2, 3, \ldots}\right\}$$.

Its LaTeX code is \mathbb{Z}^*.

The Set of Coprime Integers Modulo m
$$\mathbb{Z}'_m$$

The set $$\mathbb{Z}'_m$$ is the set of all integers modulo $m$ which are prime to $$m$$: $$\mathbb{Z}'_m = \left\{{\left[\!\left[{k}\right]\!\right]_m \in \mathbb{Z}_m: k \perp m}\right\}$$.

See Set of Coprime Integers.

Its LaTeX code is \mathbb{Z}'_m.

The Set of Integer Multiples
The set $$n \mathbb{Z}$$ is defined as $$\left\{{x \in \mathbb{Z}: n \backslash x}\right\}$$ for some $$n \in \mathbb{N}$$.

That is, it is the set of all integers which are divisible by $$n$$, that is, all multiples of $$n$$.

Its LaTeX code is n \mathbb{Z}.