The Euler's totient φ is known to be multiplicative. Letfbe de_ned byf(n) = φ (φ (n)). Is the

functionfmultiplicative? Prove your answer.

Printable View

- Aug 20th 2012, 07:38 PMmusngiburgerProving on Euler's totient?
The Euler's totient φ is known to be multiplicative. Let

*f*be de_ned by*f*(n) = φ (φ (n)). Is the

function*f*multiplicative? Prove your answer. - Aug 20th 2012, 08:44 PMDevenoRe: Proving on Euler's totient?
f will be multiplicative if gcd(a,b) = 1 implies gcd(φ(a),φ(b)) = 1. can you think of a counter-example? look at f(15).

- Sep 3rd 2012, 11:02 PMwauwauRe: Proving on Euler's totient?
@musngiburger

since $\displaystyle \varphi(n)$ is always even for n>2 $\displaystyle gcd(\varphi(a),\varphi(b)) = 1$ never true !!!!!!