Prove that Z_m is a field iff m is a prime.

Hi,

**problem:**

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 ?

**attempt:**

(a) I could really use a hint or two on this one..

(b)

Answer: 4.

(c)

Answer:5.

Btw, is there a nice math symbol for "the remainder of"?

Thanks.