Section 9.2: Computing phi(n): A Special Case

9.2 Computing (n): A Special Case

As has become our standard practice, we will work towards a general solution to our problem by starting with special cases that are easier to tackle. In this section, we consider the values of (n) when n is a power of a prime.

Research Question 1

Find a formula for (p), where p is prime.

Research Question 2

Find a formula for (p^a), where p is a prime and a is a positive integer.

Hint: You may find it easier to count the number of m p^a such that gcd(m, p^a) > 1, and subtract this from n = p^a.

Section 9.1 | Section 9.2 | Section 9.3 | Section 9.4
Chapter 9 | DNT Table of Contents