Help with proving that $\phi(n)$ $\ge$ ${\sqrt n} \over 2$
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
17231
How I can prove that the sequence $\sqrt{2} , \sqrt{2\sqrt{2}}, \sqrt{2\sqrt{2\sqrt{2}}}$ converges to 2?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
880
Find all n such that $\phi(n) = n/2$
42842
Proof for $\epsilon$ closeness to $\sqrt{2}$ for all values of $\epsilon$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
101371
show that $f^{(3)}(c) \ge 3$ for $c\in(-1,1)$
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
118244
An $n$th root inequality: $\sqrt[n]{n} < 1 + \sqrt{2/n}$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$