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# a) Generalize the result in part (a) of Exercise 16; that ISBN: 9780073383095 37

## Solution for problem 18E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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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)?

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##### ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 18E from 4.4 chapter was answered, more than 277 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 18E from chapter: 4.4 was answered by , our top Math solution expert on 06/21/17, 07:45AM. The answer to “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)?” is broken down into a number of easy to follow steps, and 105 words. This full solution covers the following key subjects: result, integers, prime, exercise, conclude. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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