Show that the phi function is multiplicative $\phi(mn) = \phi(m)\phi(n)$
58188
What's the proof that the Euler totient function is multiplicative?
53263
Show $\sum\limits_{d|n}\phi(d) = n$.
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
62111
Functional Equation $f(mn)=f(m)f(n)$.
35034
Multiplicative inverses for $Z_n$
84930
How to justify $\phi(n) \ge \sqrt{n}$
82448
Why is $f(x) = x\phi(x)$ one-to-one?
154076
How to show this property of $\mathbb{RP}^{n}$.
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
4530
For which natural numbers are $\phi(n)=2$?
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
135219
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
53745
Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
60284
Infinitely many positive integers $n$ such that $\phi(n) = \frac{n}{4}$?
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$