Proving $r!$ divides the product of r succesive positive integers
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
28658
$R$ with an upper bound for degrees of irreducibles in $R[x]$
150156
Proving that $S_n$ has order $n!$
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
46431
Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
66946
show that $(i+k)! > i!k!$ algebraically
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
27147
Proving $n! > n^3$ for all $n > a$
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
10976
Using induction to prove that $\sum_{r=1}^n r\cdot r! =(n+1)! -1$
50413
Proof: if $p$ is prime, and $0<k<p$ then $p$ divides $\binom pk$
32772
Proving units in a ring