Proof that $\frac {(2n)!}{n! 2^n}$ is integer
42062
Interpretation of a combinatorial expression
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
80216
Prove if $n \in \mathbb N$, then $\frac{1}{2!}+\cdots+\frac{n}{(n+1)!}=1-\frac{1}{(n+1)!}$
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
83313
Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$
6943
Idea behind proof that $\frac{21n+4}{14n+3}$ is irreducible for all $n$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
9920
$(n^2 - 1)!$ is a multiple of $(n!)^n$
22073
Prove by induction that $n^2<n!$
138683
Proving $\prod_{i=2}^{i=n} \left(1-\frac{1}{i^2}\right) = \frac{n+1}{2n}$ by induction
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
141837
Proof of $\sup\{ (n!)^{(\frac{1}{n})}| n ∈ N\} = +∞?$
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
56474
An example where $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is the number of ways of counting something?