Is there a more elegant answer to proving $\prod_{0\le i<j\le n-1}\frac{a_{j}-a_{i}}{j-i}$ is integer given $a_i$ is integer for $0\le i \le n-1$
7802
Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer
54055
Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
93085
How to prove the identity $\prod_{n=1}^{\infty} (1-q^{2n-1}) (1+q^{n}) =1 $ for $|q|<1$?
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
37484
Is there an elementary argument to show that $\prod_{n=0}^\infty \frac{2n+1}{2n+3}=0$
108298
Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
156646
If $x$ is rational then $\,x+\frac{1}x \,$ is an integer $\iff x = \pm 1$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
83280
Infinite product $ \prod^{\infty}_{n=0}\left(1-\frac{1}{2^{3n}}-\frac{1}{2^{6n}}\right)$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
75123
If $p$ be a prime and r be any integer, $0 < r < p$ then $\frac{(p-1)!}{r!(p-r)!}$ is an integer.
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
91081
Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$
10902
Showing that $ \prod\limits_{i=0}^{n} {n \choose i}\leq(\frac{2^n-2}{n-1})^{n-1} $