The divisibility of a particular case of $\binom{x}{y}$ (when $(x,y) = 1$)
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
63893
Prime dividing the binomial coefficients
155150
Division of Factorials [binomal coefficients are integers]
119891
Divisibility and the Fibonacci sequence
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
71625
Divisibility question
90904
Combinatorial proof of an identity with squared binomial coefficients
11470
Divisibility of integers
110876
Prove that $p\mid \binom{p}{k},\ 0< k< p$
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
124890
Divisibility within a block of natural numbers
75910
Combinatorial Proof of Combinatorial Identity involving $(-1)^k \binom {n-1}{k}$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
114277
Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$