query: Find all positive integers $n$,$m$ with $n! = \frac{m(m-1)}{2}$
positive_passages.docid: 63314
positive_passages.text: Triangular Factorials
negative_passages.docid: 98946
negative_passages.text: Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
negative_passages.docid: 32544
negative_passages.text: Give an example of three positive integers m, n, and r
negative_passages.docid: 158124
negative_passages.text: Sum of all the positive integers problem
negative_passages.docid: 7894
negative_passages.text: Does it follow that $(n!)^n$ divide $(n^2)!$
negative_passages.docid: 34374
negative_passages.text: Simplifying factorials: $\frac{(n-1)!}{(n-2)!}$
negative_passages.docid: 116901
negative_passages.text: Monotonicity of $\frac{n}{\sqrt[n]{(n!)}}$
negative_passages.docid: 20691
negative_passages.text: prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
negative_passages.docid: 104920
negative_passages.text: Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
negative_passages.docid: 91197
negative_passages.text: Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 35611
negative_passages.text: How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
negative_passages.docid: 90789
negative_passages.text: Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
negative_passages.docid: 56474
negative_passages.text: An example where $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is the number of ways of counting something?
negative_passages.docid: 106380
negative_passages.text: What is $n!$ when $n=0$?
negative_passages.docid: 113248
negative_passages.text: Proving $r!$ divides the product of r succesive positive integers
negative_passages.docid: 106888
negative_passages.text: Factorial identity $n!=1+(1-1/1!)n+(1-1/1!+1/2!)n(n-1)+\cdots$