For which $n$, $2^{n-1}\mid n!$?
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
4970
For $n \geq 2$, show that $n \nmid 2^{n}-1$
142981
Computing $n!\int...\int_{0<s_1<...<s_n}1ds_1...ds_n$
94291
$\frac{2^{2n}}{2n} \le {2n \choose n}$?
5206
Highest power of a prime $p$ dividing $N!$
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
117039
How to show $(1/n!)^{1/n}$ goes to $0$ as $n$ goes to infinity?
24572
Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?
114404
For which positive integer values of $n$ does $a|mn-b?$
133819
How to prove that $364 \mid n^{91} - n^7$?
94983
Can an odd number $n$ divide $2^n-1$?
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
139659
Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
54442
Sum of $k {n \choose k}$ is $n2^{n-1}$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction