Set symbol clarification

Question

Quick question, which set does this notation imply?

$${\mathbb{Z}^3_5}$$

Could you make an exmple?

Thanks in advance

Answer 1

In one context, for example, $\mathbb{Z}_5$ would mean a set $\{0,1,2,3,4\}$ with the usual additive arithmetic modulo $5$ defined on it.

Similarly, $\mathbb{Z}_5^3$ would mean a 3-dimensional set of vectors, each element of which comes from $\mathbb{Z}_5$, so $$ \mathbb{Z}_5^3 = \left\{ (a,b,c) | a,b,c \in \mathbb{Z}_5\right\} $$

Answer 2

It probably means $\mathbb Z_5 \times\mathbb Z_5 \times\mathbb Z_5$, where $\mathbb Z_5$ means $\mathbb Z/5\mathbb Z$.

In other words, $(\mathbb Z_5)^3$.