   Chapter 7.1, Problem 51ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# 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.Find each of the followingaa. ϕ (15)b. ϕ (2)c. ϕ (5)d. ϕ (12)e. ϕ (11)e. ϕ (1)

To determine

(a)

To calculate:

ϕ(15).

Explanation

Given information:

ϕ(n) is the number of positive integers less than or equal to n that have no common factors with n except ±1.

Calculation:

To find ϕ(15), first find the positive integers less than or equal to 15 that have no common factors with 15 except ±1.

Thus, ϕ(15)=8

To determine

(b)

To find:

ϕ(2).

To determine

(c)

To evaluate:

ϕ(5).

To determine

(d)

To calculate:

The value of ϕ(12).

To determine

(e)

To find:

The value of ϕ(11).

To determine

(f)

To evaluate:

The value of ϕ(1).

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