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Thread: Euler's totient

  1. #1
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    Euler's totient

    Suppose p and q are unequal primes. Prove the following:

    a. pi(p)=p-1
    b. pi(p^2)=p^2-p
    c. pi(p^n)=p^n-p^n-1 where n is a positive integer
    d. pi(pq)=pq-q-p+1 = (p-1)(q-1)
    Last edited by teramaries; Jun 30th 2010 at 04:54 PM. Reason: mistake
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by teramaries View Post
    Suppose p and q are unequal primes. Prove the following:

    a. pi(p)=p-1
    b. pi(p^2)=p^2-p
    c. pi(p^n)=p^n-p^n-1 where n is a positive integer
    d. pi(pq)=pq-q-p+1 = (p-1)(q-1)
    Just list all the numbers less than or equal to the input of $\displaystyle \varphi $ and count how many are divisible by the input.
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