# Recent content by hegelec

1. ### Euler, phi and division

Here's how I did it. Prove that if m | n, then phi(m) | phi(n) Note that from phi(p^a) = (p^(a-1))(p-1) for some prime p, it follows that phi(p^a) | phi(p^b) for a | b. This generalizes to phi(k^a) | phi(k^b) for composite k, since phi is multiplicative. Since m | n, there exists some q...
2. ### Euler, phi and division

There is a crucial problem with your tactic, namely that the Euler phi function is ONLY multiplicative for co-primes. Consider that 2|8. 8=2*4, but 2 and 4 are not co-prime. Phi(2)=1 and Phi(4)=2. Phi(2)*Phi(4)=2. But Phi(8)=4! Multiplicativity of Phi alone is sufficient to prove the property...