# Euler's totient function

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• Dec 8th 2008, 06:54 PM
Rafael Almeida
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,
• Dec 8th 2008, 09:53 PM
ThePerfectHacker
Quote:

Originally Posted by Rafael Almeida
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.