 # Each of exercises 51-53 refers to the Euler phi function, denoted ϕ , which is defined as follows: For each integer n ≥ 1 , ϕ ( n ) is the number of positive integers less than or equal to n that have no common factors with n except ± 1 . For example, ϕ ( 10 ) = 4 because there are four positive integers less than or equal to 10 that have no common factor with 10 except ± 1 -namely, 1,3,7, and9. Prove that if p is a prime number and n is an integer with n ≥ 1 , then ϕ ( p n ) = p n − p n − 1 . ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193 ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
Publisher: Cengage Learning,
ISBN: 9781337694193

#### Solutions

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Chapter 7.1, Problem 52ES
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