List questions from binomial-coefficients

Published on 10 Apr 2026 - 21:47

258

Views

Show that there are infinitely many integers such that $ \binom{m}{n-1} = \binom{m-1}{n} $

Published on 16 Apr 2026 - 2:15

50

Views

Production process testing - binomial probabilities

Published on 09 Apr 2026 - 13:29

114

Views

What are all the even positive integers $n$ such that for $1 \le r \le n-1 $ , $2n \choose r$ is odd for exactly one $r$ ?

Published on 12 Apr 2026 - 4:36

407

Views

To prove ${2p - 1 \choose p } \equiv 1 \pmod{p^2}$ without using Wolstenholme's theorem

Published on 16 Apr 2026 - 14:32

2.8k

Views

How to deal with this double summation?

Published on 11 Apr 2026 - 19:54

89

Views

How can I compute $\sum\limits_{k = 1}^n \binom{n - 1}{k - 1}$?

Published on 09 Apr 2026 - 11:35

229

Views

Use of Multinomial theorem.

Published on 26 Mar 2026 - 9:38

89

Views

To prove for every integer $k >1 $ , $2+2^k \choose r$ is even for all $2 < r \le n=1+2^{k-1}$ , without Lucas' theorem

Published on 15 Apr 2026 - 10:27

259

Views

Proof verification ($p$ prime then $p\mid \binom{p}{k}$ for $1\le k\le p-1$)

Published on 14 Apr 2026 - 2:22

65

Views

Express $\binom{n+2}{k}$ according to $\binom{n}{k}$

Published on 14 Apr 2026 - 16:54

52

Views

Compute convolution

Published on 17 Apr 2026 - 13:37

147

Views

Approximating a binomial sum over a simplex

Published on 14 Apr 2026 - 13:33

1.9k

Views

Proof by induction (combinations): $\binom n1 =n$ and $\binom n{n-1}=n$

Published on 15 Apr 2026 - 10:08

1.2k

Views

How to expand $(x+y)^{-n}$?

Published on 13 Apr 2026 - 14:19

List Question

Simpler expression for binomial sum

Show that there are infinitely many integers such that $ \binom{m}{n-1} = \binom{m-1}{n} $

Production process testing - binomial probabilities

What are all the even positive integers $n$ such that for $1 \le r \le n-1 $ , $2n \choose r$ is odd for exactly one $r$ ?

To prove ${2p - 1 \choose p } \equiv 1 \pmod{p^2}$ without using Wolstenholme's theorem

How to deal with this double summation?

How can I compute $\sum\limits_{k = 1}^n \binom{n - 1}{k - 1}$?

Use of Multinomial theorem.

To prove for every integer $k >1 $ , $2+2^k \choose r$ is even for all $2 < r \le n=1+2^{k-1}$ , without Lucas' theorem

Proof verification ($p$ prime then $p\mid \binom{p}{k}$ for $1\le k\le p-1$)

Express $\binom{n+2}{k}$ according to $\binom{n}{k}$

Compute convolution

Approximating a binomial sum over a simplex

Proof by induction (combinations): $\binom n1 =n$ and $\binom n{n-1}=n$

How to expand $(x+y)^{-n}$?

Trending Questions

Popular # Hahtags

Popular Questions