Question

Remainders of factorials modulo primes

score 41 · Answer 1 · 2024-02-18 11:03:15

41

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Remainders of factorials modulo primes

Published on 18 Feb 2024 - 11:03

score 45 · Answer 2 · 2026-03-25 11:53:20

45

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Matrix involving reciprocal factorials

Published on 25 Mar 2026 - 11:53

score 306 · Answer 3 · 2026-03-29 07:19:37

306

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Prove that Wallis' product and Euler's formula directly imply that $(-1/2)!=\sqrt{\pi}$

Published on 29 Mar 2026 - 7:19

score 54 · Answer 4 · 2024-02-23 22:14:32

54

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limit of sequence $\{a_n\}$ where $a_n = n!/c^n$, as $n$ tends to infinity

Published on 23 Feb 2024 - 22:14

score 49 · Answer 5 · 2026-04-01 06:22:03

Prove $\frac{(n/2)!(n/2)!}{\left(\frac{n+i}2\right)!\left(\frac{n-i}2\right)!}=\prod_{j=1}^{i/2}\frac{\frac n2+1-j}{\frac n2+j}$

score 204 · Answer 6 · 2024-02-29 14:45:51

204

Views

Showing $ \frac{2^j(2k-j)!}{(k-j)!}=\sum_{l=j}^k\frac{2^ll(2k-l-1)!}{(k-l)!} $

Published on 29 Feb 2024 - 14:45

score 73 · Answer 7 · 2026-03-25 06:22:08

73

Views

Theater Seating Combinatorics Problem: 6 friends go to the movies and sit in adjoining seats in one row

Published on 25 Mar 2026 - 6:22

score 32 · Answer 8 · 2024-03-06 08:12:17

32

Views

Proof that $\left(\frac{{\pi}^n}{nn!}\right)_{n\ge 1}$ is a decreasing sequence

Published on 06 Mar 2024 - 8:12

score 50 · Answer 9 · 2024-03-07 11:41:38

50

Views

How to set equations containing factorials?

Published on 07 Mar 2024 - 11:41

score 113 · Answer 10 · 2026-03-31 20:07:07

113

Views

Limit $\lim_{n\to +\infty}{\frac{\left(n!\right)^2\cdot4^n\cdot n}{\left(2n\right)!}}$

Published on 31 Mar 2026 - 20:07

score 498 · Answer 11 · 2024-03-10 20:42:22

498

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Is there a prime number $p$ dividing $1+2!^2+3!^2+\cdots (p-1)!^2$?

Published on 10 Mar 2024 - 20:42

score 116 · Answer 12 · 2024-03-15 22:57:50

116

Views

Is it possible to re-arrange LHS for $x$ or $y$ in the equation $x(y!)(x!)y=q$?

Published on 15 Mar 2024 - 22:57

score 72 · Answer 13 · 2024-03-17 14:49:23

72

Views

Ways To Order Matches - Six Nations

Published on 17 Mar 2024 - 14:49

score 66 · Answer 14 · 2024-03-23 23:24:38

66

Views

How does $(k+1)!(k+2)(k+1)$ simplify to $(k+2)!(k+1)$

Published on 23 Mar 2024 - 23:24

score 451 · Answer 15 · 2026-03-31 11:31:34

451

Views

Prime factor wanted of the huge number $\sum_{j=1}^{10} j!^{j!}$

Published on 31 Mar 2026 - 11:31

List Question

Remainders of factorials modulo primes

Matrix involving reciprocal factorials

Prove that Wallis' product and Euler's formula directly imply that $(-1/2)!=\sqrt{\pi}$

limit of sequence $\{a_n\}$ where $a_n = n!/c^n$, as $n$ tends to infinity

Prove $\frac{(n/2)!(n/2)!}{\left(\frac{n+i}2\right)!\left(\frac{n-i}2\right)!}=\prod_{j=1}^{i/2}\frac{\frac n2+1-j}{\frac n2+j}$

Showing $ \frac{2^j(2k-j)!}{(k-j)!}=\sum_{l=j}^k\frac{2^ll(2k-l-1)!}{(k-l)!} $

Theater Seating Combinatorics Problem: 6 friends go to the movies and sit in adjoining seats in one row

Proof that $\left(\frac{{\pi}^n}{nn!}\right)_{n\ge 1}$ is a decreasing sequence

How to set equations containing factorials?

Limit $\lim_{n\to +\infty}{\frac{\left(n!\right)^2\cdot4^n\cdot n}{\left(2n\right)!}}$

Is there a prime number $p$ dividing $1+2!^2+3!^2+\cdots (p-1)!^2$?

Is it possible to re-arrange LHS for $x$ or $y$ in the equation $x(y!)(x!)y=q$?

Ways To Order Matches - Six Nations

How does $(k+1)!(k+2)(k+1)$ simplify to $(k+2)!(k+1)$

Prime factor wanted of the huge number $\sum_{j=1}^{10} j!^{j!}$

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