how prove $\phi(n)\ge \frac{n}{6\log \log (n)} $ $\forall n\ge5 $
34960
Lower bound for $\phi(n)$: Is $n/5  1$?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
117681
For which Natural $n\ge2: \phi(n)=n/2$
106502
Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
119118
Prove $n\mid \phi(2^n-1)$
21151
$\log(n)$ is what power of $n$?
137609
Proving $\lim_{n\rightarrow\infty} n(2^{1/n} - 1) = \log 2$
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?
53745
Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$
84930
How to justify $\phi(n) \ge \sqrt{n}$
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
9753
How to solve the equation $\phi(n) = k$?
125680
Show that $(1+u) \log (1+u) - u \ge \frac{u^2}{2(1+u/3)} $
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
30897
$\pi(x)\geqslant\frac{\log x}{2\log2}$ for all $x\geqslant2.$