Question

IMO/1981 - Combinatorics

score 252 · Answer 1 · 2026-03-19 16:18:23

252

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IMO/1981 - Combinatorics

Published on 19 Mar 2026 - 16:18

score 50 · Answer 2 · 2026-03-20 11:27:02

50

Views

Divisibility of binomial coefficient

Published on 20 Mar 2026 - 11:27

score 159 · Answer 3 · 2026-03-24 22:08:17

159

Views

Closed form for square of binomial CDF

Published on 24 Mar 2026 - 22:08

score 166 · Answer 4 · 2026-03-25 01:17:20

166

Views

Sum identity over the reciprocal of central binomial coefficients using their partial fraction decompositions.

Published on 25 Mar 2026 - 1:17

score 146 · Answer 5 · 2026-03-22 23:01:51

146

Views

How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

Published on 22 Mar 2026 - 23:01

score 178 · Answer 6 · 2026-03-20 05:21:38

178

Views

$\sum\limits_{k=0}^{\frac{n}{2}} 2k\binom{n}{2k}=n\cdot2^{n-2}$

Published on 20 Mar 2026 - 5:21

score 282 · Answer 7 · 2026-03-25 01:18:09

282

Views

How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

Published on 25 Mar 2026 - 1:18

score 316 · Answer 8 · 2026-03-20 07:47:07

316

Views

If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Published on 20 Mar 2026 - 7:47

score 259 · Answer 9 · 2026-03-19 21:39:35

259

Views

Expected value of obtained dice faces by rolling a n-faced dice repeatedly

Published on 19 Mar 2026 - 21:39

score 846 · Answer 10 · 2026-03-20 05:35:23

846

Views

Determine the coefficient of $x^6$ in $(1 - x)^{15}$

Published on 20 Mar 2026 - 5:35

score 152 · Answer 11 · 2026-03-17 21:46:18

152

Views

A rational function with hidden symmetry and alternating poles and zeros.

Published on 17 Mar 2026 - 21:46

score 903 · Answer 12 · 2026-03-20 01:32:29

903

Views

Use a generating function to find the number of ways to distribute $r$ jelly beans among $8$ children if each child gets at least one jelly bean.

Published on 20 Mar 2026 - 1:32

score 356 · Answer 13 · 2026-03-19 23:15:45

356

Views

Binomial coefficient: Search for multiples of 13

Published on 19 Mar 2026 - 23:15

score 1.4k · Answer 14 · 2026-03-20 01:16:25

1.4k

Views

Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$

Published on 20 Mar 2026 - 1:16

score 74 · Answer 15 · 2026-03-19 21:28:00

74

Views

Show that you can choose a subset of these binomial coefficients whose gcd is $1$

Published on 19 Mar 2026 - 21:28

List Question

IMO/1981 - Combinatorics

Divisibility of binomial coefficient

Closed form for square of binomial CDF

Sum identity over the reciprocal of central binomial coefficients using their partial fraction decompositions.

How to prove that if $n$ is prime then ${{n}\choose{i}} = 0 \mod{n}$?

$\sum\limits_{k=0}^{\frac{n}{2}} 2k\binom{n}{2k}=n\cdot2^{n-2}$

How many rational numbers are in the opening of this binomial: $(\sqrt3+\sqrt[3]2)^{100}$

If $n$ is a multiple of $8$, then the number of sets of size divisible by $4$ is $2^{n-2} + 2^{(n-2)/2}$

Expected value of obtained dice faces by rolling a n-faced dice repeatedly

Determine the coefficient of $x^6$ in $(1 - x)^{15}$

A rational function with hidden symmetry and alternating poles and zeros.

Use a generating function to find the number of ways to distribute $r$ jelly beans among $8$ children if each child gets at least one jelly bean.

Binomial coefficient: Search for multiples of 13

Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$

Show that you can choose a subset of these binomial coefficients whose gcd is $1$

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