query: For integer $n>2$, $(n!)^2 > n^n$
positive_passages.docid: 2554
positive_passages.text: Show that if $n>2$, then $(n!)^2>n^n$.
negative_passages.docid: 45645
negative_passages.text: Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
negative_passages.docid: 66946
negative_passages.text: show that $(i+k)! > i!k!$ algebraically
negative_passages.docid: 54369
negative_passages.text: Proof of $n^2 \leq 2^n$.
negative_passages.docid: 4750
negative_passages.text: Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
negative_passages.docid: 152870
negative_passages.text: Near integers in powers of binomials with radicals
negative_passages.docid: 10742
negative_passages.text: Powers of prime factors of a positive integer $n$ in "Mathematica"?
negative_passages.docid: 20964
negative_passages.text: Proof that $n^2 < 2^n$
negative_passages.docid: 144732
negative_passages.text: If $[G:H]=n$, then $g^{n!}\in H$ for all $g\in G$.
negative_passages.docid: 22073
negative_passages.text: Prove by induction that $n^2<n!$
negative_passages.docid: 61117
negative_passages.text: Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
negative_passages.docid: 42292
negative_passages.text: Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
negative_passages.docid: 13739
negative_passages.text: For all $n>2$ there exists a prime number between $n$ and $ n!$
negative_passages.docid: 8609
negative_passages.text: Prove by induction that $n!>2^n$
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 97684
negative_passages.text: Show $\frac{(2n)!}{n!\cdot 2^n}$ is an integer for $n$ greater than or equal to $0$
negative_passages.docid: 10604
negative_passages.text: Prove $3^n > n^2$ by induction