Problem 3: Let Z8 be the set of equivalence classes of integers mod 8, i.e. the...

Transcribed Image Text:

Problem 3: Let Z8 be the set of equivalence classes of integers mod 8, i.e. the quotient of Z by the equivalence relation m ~n if 8 divides m - n. (a): Show that multiplication is well-defined on Z8, that is, that mn mod 8 only depends on m mod 8 and n mod 8. (b):If n is an integer, what are the possible values of n mod 8? Problem 3: Let Z8 be the set of equivalence classes of integers mod 8, i.e. the quotient of Z by the equivalence relation m ~n if 8 divides m - n. (a): Show that multiplication is well-defined on Z8, that is, that mn mod 8 only depends on m mod 8 and n mod 8. (b):If n is an integer, what are the possible values of n mod 8?