   Chapter 2.8, Problem 23E

Chapter
Section
Textbook Problem

The Euler phi-function is defined for positive integers n as follows: ϕ ( n ) is the number of positive integers m such that   1 ≤ m ≤ n and ( m ,   n )   =   1 . Evaluate each of the following and list each of the integers m relatively prime to the given n . ϕ ( 5 ) ϕ ( 19 ) ϕ ( 15 ) ϕ ( 27 ) ϕ ( 12 ) ϕ ( 36 )

(a)

To determine

ϕ(5) and list each of the integers m relatively prime to 5.

Explanation

Given information:

The Euler phi- function is defined for positive integer n as follows: ϕ(n) is the number of positive integers m, such that 1mn and (m,n)=1.

Explanation:

By using the definition of Euler phi- function, find m, such that, 1m5 and

(b)

To determine

ϕ(19) and list each of the integers m relatively prime to 19.

(c)

To determine

ϕ(15) and list each of the integers m relatively prime to 15.

(d)

To determine

ϕ(27) and list each of the integers m relatively prime to 27.

(e)

To determine

ϕ(12) and list each of the integers m relatively prime to 12.

(f)

To determine

ϕ(36) and list each of the integers m relatively prime to 36.

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