Prove that sgn$(\sigma \tau) = $sgn$(\sigma)$sgn$(\tau)$
102398
Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
108298
Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
67949
$S_3$ permutes the elements of $\mathbb{R}^3$, show that $\sigma (x_1, x_2, x_3) = ( x_{\sigma^{-1}(1)}, x_{\sigma^{-1}(2)}, x_{\sigma^{-1}(3)})$.
69715
Proving $\text{Var}{(\hat{y}_h)} = \sigma^2 \left(\frac{1}{n} + \frac{(x_h-\bar{x})^2}{S_{xx}}\right)$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
33144
Criterion for $\phi(mn)=m\phi(n)$ to be true
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
125894
Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
110450
probability measure on $\sigma$-algebra
44575
The sigma function (sum of divisors) multiplicative proof
14383
Order of Permutation : If $\tau \in S_n$ has order $m$, then $\sigma \tau\sigma^{-1}$ has also order $m$.
110103
Prove that there are $0<c_1 < c_2<1$ s.t. $\frac{1}{g'(c_1)}+\frac{1}{g'(c_2)}=2$ . The same for $g'(c_1)g'(c_2)=1$.
158582
Prove that $\{\frac{\phi (n)}{n}\}_{n \in \Bbb N}$ is dense in $[0,1]$
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
137446
Show that if $b_k\uparrow \infty$ and $\Sigma_{k = 1}^\infty a_kb_k$ converges, then $b_m \Sigma_{k = m}^\infty a_k → 0$ as $m → \infty$.