What is the value of ?(pk) when p is prime and k is a positive integer?
Step 1 of 3
Solution:-Step1Given thatWhen k is a positive integer and p is prime,we have to calculate the value of ()Step2The value of the Euler's function number of the positive integers up to a given integer m that are relatively prime to m.if gcd(then integers are relatively prime Where From question Step3Given that p is a prime number.So, the only positive factors of p are 1 and p.So, other than 1, positive factors will beStep4So,gcdAlsogcdSo, the value of the Euler’s function = Therefore, the value of () when p is prime and k is a positive integer is .
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
This full solution covers the following key subjects: Integer, Positive, prime. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The full step-by-step solution to problem: 23E from chapter: 4.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. Since the solution to 23E from 4.3 chapter was answered, more than 323 students have viewed the full step-by-step answer. The answer to “What is the value of ?(pk) when p is prime and k is a positive integer?” is broken down into a number of easy to follow steps, and 16 words.