Question: Fix m, n N . Define a mapping f : Z/nZZ/mZ by f([a] n ) = [a] m . a. Prove that if m |

Fix m, n N . Define a mapping f : Z/nZZ/mZ by f([a]n) = [a]m.

a. Prove that if m | n then f is a well-defined function. That is, prove that if [a]n= [b]n then f([a]n) =f([b]n).

b. Let n = 12 and m = 3. Write PreImf({[1]3,[2]3}) in roster notation.

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