What does it mean to prove that a set of binary integers is regular? I'm not exactly sure what this question is asking me to do:


  Show that the set of binary integers (given as strings over $\{0, 1\}$) that are divisible by $3$ is regular, by giving a DFA that recognizes it. Leading 0s are allowed. The empty string should be accepted. Briefly explain your answer.


Is this asking me to construct a DFA where the set of binary integers add up to be divisible or the number of elements is divisible?

I understand that by constructing the DFA I prove that it is regular.
The question asks you to construct a DFA for the language

$$L = \{x \in \{0,1\}^* : x \text{ is the binary representation of an integer that is divisible by three}\}.$$

In other words, the DFA should accept a string if and only if this string is the binary representation of a number that is divisible by three.