Let $p$ be a prime. Why is ${p^mn \choose p^m}$, where $p \nmid n$, not divisible by $p$?
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
63493
Why 4 is not a primitive root modulo p for any prime p?
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
130615
divisibility of binomial coefficients by primes
5206
Highest power of a prime $p$ dividing $N!$
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
16459
Limit of ratios of numbers with $m$ factors and primes
131551
$pq\mid pn^q+qn^p+kn$ for some $k,\,$ if $p,q$ are primes
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
92737
primes whose difference is a multiple of $n$
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
68328
Infinitely many $n$ such that $2^n-n$ is divisible by a prime
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?