# Euler's totient function

• Dec 8th 2008, 05:54 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 $\displaystyle n$ such that $\displaystyle \varphi(n) = pq$, where p and q are prime.
2. Find all positive numbers $\displaystyle n$ such that $\displaystyle \varphi(n) = 8$

How do I approach these? Any tips are welcome.

• Dec 8th 2008, 08:53 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 $\displaystyle n$ such that $\displaystyle \varphi(n) = pq$, where p and q are prime.
2. Find all positive numbers $\displaystyle n$ such that $\displaystyle \varphi(n) = 8$

How do I approach these? Any tips are welcome.

Write $\displaystyle n=p_1^{a_1}...p_k^{a_k}$ and now apply formula for $\displaystyle \phi (n)$.
After that compare sides and see what $\displaystyle n$ got to be.
Also for (1) it seems that $\displaystyle p,q$ are odd primes because $\displaystyle \phi(n) = 14$ has no solutions.