Question on the Euler phi funtion.
53426
Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$
47790
If $x \geq 2$ prove that $\sum_{ n \leq x} \frac{1}{\phi(n)} = \mathcal{O}(\log(x))$
91889
Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
37346
If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$.
81346
Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$.
151111
How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?
140990
Could anyone explain to me how did we get this result? This is simple example but I'm struggling with little o notation in general.
137982
Show that $\textbf{ZF}$ shows $\phi$ is $\Delta_1$
135219
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
17178
Order of $\phi(g)$ divides the order of $g$
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
8784
modulo version of the quadratic formula and Euler's criterion
12949
Inductive Proof of Euler's Formula $v-e+r=2$
12976
Prove $\displaystyle\lim_{n\to\infty}\phi(n)=\infty$.
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
158515
Identity involving Euler's totient function: $\sum \limits_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \varphi(k) = \frac{n(n+1)}{2}$