Let m, n be positive integers with m | n, and let k be any integer. Show that f :

Zn-> Zm defined by f([x]n) = [x]m^k, for all [x]n belong to Zn

is a well-defined function.

Hint: We know that g : Z×

m ! Z×

m defined by g([x]m) = [x]k

m is a function if k is a

positive integer.