If $0 < i < p$, then $p \mid \binom{p}{i}$
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
104704
Evaluate $\sum\limits_{k=0}^n \binom{n}{k}$ combinatorially
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
140829
What does $b_i\mid b_{i+1}$ mean in this context?
116215
Prove that $P(A \cap B\mid C)=P(A \mid (B \cap C))P(B\mid C)$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
69515
If $x_n\cdot y_n\to 0$ then $x_n \to 0$ or $y_n \to 0 $
49783
A possible inequality related to binomial theorem (or, convex/concave functions)
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
107335
Prove equality between binomial coefficients.
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
117761
When is $\binom{n}{k}$ divisible by $n$?
147079
$\gcd\left(\binom{n}{k},n\right)>1$ for nontrivial values?
54905
A classical inequality involving the central binomial coefficient
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
153107
Does every connected component of $\{z : |P(z)|<1 \}$ contain a zero?