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Math Help - Euler's totient function

  1. #1
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    Euler's totient function

    Hi all again,

    Now the problem is with Euler's Function. See:

    1. Find all positive and integer n such that \varphi(n) = pq, where p and q are prime.
    2. Find all positive numbers n such that  \varphi(n) = 8

    How do I approach these? Any tips are welcome.

    Thanks in advance,
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  2. #2
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    Quote Originally Posted by Rafael Almeida View Post
    Hi all again,

    Now the problem is with Euler's Function. See:

    1. Find all positive and integer n such that \varphi(n) = pq, where p and q are prime.
    2. Find all positive numbers n such that  \varphi(n) = 8

    How do I approach these? Any tips are welcome.

    Thanks in advance,
    Write n=p_1^{a_1}...p_k^{a_k} and now apply formula for \phi (n).
    After that compare sides and see what n got to be.

    Also for (1) it seems that p,q are odd primes because \phi(n) = 14 has no solutions.
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