$\frac{(10!)!}{(10!)^{9!}}$ is an integer
87843
Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer
139776
Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
14815
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
132732
Estimate of n factorial: $n^{\frac{n}{2}} \le n! \le \left(\frac{n+1}{2}\right)^{n}$
122020
What is the remainder when $1! + 2! + 3! +\cdots+ 1000!$ is divided by $12$?
155005
How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
122530
Number of zeros at the end of $k!$
12250
How to find the prime factorization of $100!$.
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
64668
Verify that $4(29!)+5!$ is divisible by $31$.
143343
The series of reciprocals of the integers that do not contain 9 in their decimal representation
118140
Prove that $ \frac{n(n-1)(n-k+1)}{k(k-1)\cdots1} = \frac{n!}{(n-1)!k!}$
8318
A positive integer (in decimal notation) is divisible by 11 $ \iff $ ...
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?