Showing that $\frac{(m+n-1)!}{m!n!}\in\mathbb{Z}$, if $m,n$ coprime (homework problem)
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
45171
How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
93031
How to show that $\mathbb{Z}$ with the operation $m*n=m+(-1)^m n$ is associative?
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
97684
Show $\frac{(2n)!}{n!\cdot 2^n}$ is an integer for $n$ greater than or equal to $0$
106888
Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
51858
Showing $\gcd(2^m-1,2^n+1)=1$
46431
Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]