# Math Help - Euler's totient function

1. ## 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.

2. 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.

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.