If $n$ is composite then $n$ divides $(n-1)!$
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
73102
Given the factors of $N$, is there a method for computing the factors of $N-1$ or $N+1$?
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
136077
Prove that $x-1$ is a factor of $x^n-1$
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
8609
Prove by induction that $n!>2^n$
117761
When is $\binom{n}{k}$ divisible by $n$?
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
117167
$3^{n+1}$ divides $2^{3^n}+1$
34374
Simplifying factorials: $\frac{(n-1)!}{(n-2)!}$
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]