Prove that Z_m is a field iff m is a prime.
Let be an integer, and let be the set of all positive integers less than , .
If and are in , let be the least positive remainder obtained by dividing the (ordinary) sum of and by ,
and similarly, let be the least positive remainder obtained by dividing the (ordinary) product of and by .
(a) Prove that is a field if and only if is a prime.
(b) What is -1 in ?
(c) What is in ?
(a) I could really use a hint or two on this one..
Btw, is there a nice math symbol for "the remainder of"?