It is me again :), I am trying to prove this statement of congruence, the statement is as follows:
$a \equiv b \mod m \Longrightarrow a^{k} \equiv b^{k} \mod m $ for all $ k \in \mathbb{N}$
i cannot even start the prove, i dont know where to start. can some please help me.
i know the definition of congruence:
$a \equiv b \mod m :\Longleftrightarrow m|a-b $
how can i use it to prove the statement? thanks