a) Generalize the result in part (a) of Exercise 16; that
Chapter 4, Problem 18E(choose chapter or problem)
Problem 18E
a) Generalize the result in part (a) of Exercise 16; that is, show that if p is a prime, the positive integers less than p, except I and p ‒ 1, can be split in to (p ‒ 3)/2 pairs of integers such that each pair consists of integers that are inverses of each other. [Him: Use the result of Exercise 17.]
b) From part (a) conclude that (p ‒ 1)! ≡ ‒ 1 (mod p) whenever p is prime. This result is known as Wilson's theorem.
c) What can we conclude if n is a positive integer such that (n ‒ 1)! ≢ ‒1 (mod n)?
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer