How to prove that $n$ divides $\binom{n}{k}$ if $n$ is prime?
75123
If $p$ be a prime and r be any integer, $0 < r < p$ then $\frac{(p-1)!}{r!(p-r)!}$ is an integer.
136580
Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$
96169
$n$ divides a product of $n$ consecutive integers (by $n$ divides one of them)
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
154722
How do I prove $2 \binom n2 + 4 \binom n4 + 6 \binom n6 + \cdots = n 2^{n-2}$
13525
Prove: If $n=2^k-1$, then $\binom{n}{i}$ is odd for $0\leq i\leq n$
116361
Relationship between prime factorizations of $n$ and $n+1$?
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
10191
Binomial theorem: divisibility by $n^2$
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number
9046
Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
80365
Prove that $n$ is divisible by $6$
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $