Symbols:Z

The Set of Integers
$$\Z$$

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

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

Its LaTeX code is \mathbb{Z} or \Z.

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

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

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

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

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

See Set of Coprime Integers.

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

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

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} or n \Z.