Integer Equation $m ! = \frac{n(n+1)}{2}$
63314
Triangular Factorials
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
112575
Finding integer solutions of $m^2-n^5 = m - n$
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
106380
What is $n!$ when $n=0$?
87843
Combinatorial proof that $\frac{({10!})!}{{10!}^{9!}}$ is an integer
63553
Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
106965
How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
115244
Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
73418
Show that $\frac{(2n)!!}{(2n+1)!!}$ converges.
26087
Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
126820
How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?
135927
Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction