i am trying to prove this statement of congruence which is not really hard, but i am stumbling across the simple step.
statement: $a \equiv b \mod m \land c \equiv d \mod m \Longrightarrow ac \equiv bd \mod m$
my steps are:
$a \equiv b \mod m \Longrightarrow a=km+b$ and $c \equiv d \mod m \Longrightarrow c=km+d$
so: $ac =(km+b)(km+d).. \Longrightarrow help$
i need help here how to come to $ac \equiv bd \mod m$
thanks for reading