Let

Z_(n)={[0]_(n),[1]_(n),dots,[n-1]_(n)}

for any natural number

n

, where

[r]_(n)

represents the equivalent class of

r

modulo\

n

. Define

f_((n,m)):Z_(n)->Z_(m)

by

f_((n,m))([r]_(n))=[r]_(m)

. Find necessary and sufficient condition on

n

and

m

that makes\

f_((n,m))

a function. Justify (prove) your answer.