When does $(p-1)! + 1 = p^k $ hold?
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
69943
why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
73997
$x^{p-1} + ... + x^2 + x + 1$ is irreducible using Eisenstein's criterion?
129536
Asymptotic behaviour of sums of consecutive powers
45171
How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
16035
Irreducibility of $X^{p-1} + \cdots + X+1$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
72735
Understanding the proof of a formula for $p^e\Vert n!$
7894
Does it follow that $(n!)^n$ divide $(n^2)!$
50596
$p_1p_2...p_n +1$ is not square for $p_k = k$'th prime
127205
Explain proof of irreducibility of $x^{p-1} + 2x^{p-2}+ \dots +(p-1)x + p$
48211
When is $(a+b)^n \equiv a^n+b^n$?
54192
Why $x^{p^n}-x+1$ is irreducible in ${\mathbb{F}_p}$ only when $n=1$ or $n=p=2$