The relation of "congruence modulo n" is the relation ≡ defined by x ≡ y mod n if and only if x mod n = y mod n.
(a) Show that congruence modulo n is an equivalence relation by showing that it defines a partition of the integers into equivalence classes.
(b) Show that congruence modulo n is an equivalence relation by showing that it is reflexive, symmetric, and transitive.
(c) Express the Chinese Remainder theorem in the notation of congruence modulo n.