Find Number of Generators in Z_(p^r)

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Let p be a prime number. Find the number of generators of the cyclic group Z_(p^r), where r is an integer >=1.

A small hint, please?
 
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What do you know about generators of cyclic groups?
 
Well, the generators are those which are relatively prime to p^r.
 
Eivind said:
Well, the generators are those which are relatively prime to p^r.
And don't you know an algorithm for computing how many integers in the range [0, n] are relatively prime to any number n?
 

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