I am studying modular arithmetic and I don't know how to prove or disprove the following :
If $x \equiv c \mod n $ then $x \equiv -c \mod n$
By trying different numbers it seems as this is true ,some attempt I've made so far is :
$x \equiv c \mod n \implies x \equiv -(-c) \mod n $
Since $-x \equiv -c \mod n $ I have that $$ x \equiv -(-x) \mod n \implies 0\equiv 0 \mod n $$
What does the last statement now mean ?