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) whennis a power of a prime.

## Research Question 1

Find a formula for

_{}(p), wherepis prime.

## Research Question 2

Find a formula for

_{}(p), where^{a}pis a prime andais a positive integer.

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

Section 9.1 | Section 9.2 | Section 9.3 | Section 9.4

Copyright © 2001 by W. H. Freeman and Company