My teacher has demonstrated this problem at class but I didn't understand at the time, and now I can't find any material in internet about this specific problem:
"How can I prove that in the finite field Zp, where p is a prime number, the only elements that are their own inverse are 1 and -1?"
I do understand Fermat's little theorem, and I know how to prove that each element has only one inverse, but I can't solve this problem. I would be very thankful if someone could help me with this.
Actually, how can I prove that in integers, the only numbers that are their own multiplicative inverses are 1 and -1?