Possible Duplicate:
Value of cyclotomic polynomial evaluated at 1
I have to show $\Phi_n(1)=1$ for $n\neq p^k$ with $p$ is prime.
(I already proved to easy part $\Phi_n(1)=p$ for $n=p^k$)
For the proof I would start with: For an arbitrary natural number $n$ we have the unique factorization of primes $n=p_1^{\beta_1}p_2^{\beta_2}\cdots p_k^{\beta_k}$ ($gcd(p_i,p_j)=1$ for $i\neq j$)
I know that there are $\beta_i$ divisors of $n$, which are the powers of each prime $p_i$ which divide $n$. But how can I say that $\Phi_d(1)=1$ for any $d$ with more than one prime divisor?