Question

Does a factorial always differ by a square from a square?

score 90 · Answer 1 · 2026-03-25 15:38:22

90

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Does a factorial always differ by a square from a square?

Published on 25 Mar 2026 - 15:38

score 114 · Answer 2 · 2018-10-20 22:55:59

114

Views

Closed form for a sum

Published on 20 Oct 2018 - 22:55

score 65 · Answer 3 · 2018-10-21 13:26:01

65

Views

Limit of $\frac{N^{n}(N!)^{n}}{(n-1)!}$ as $n$ tends to infinity

Published on 21 Oct 2018 - 13:26

score 103 · Answer 4 · 2018-10-22 20:16:03

103

Views

Trying to prove : $n! ≥ (n/2)^{n/2}$

Published on 22 Oct 2018 - 20:16

score 244 · Answer 5 · 2018-10-25 03:40:43

244

Views

Which grows at a faster rate $\sqrt {n!}$ vs $(\sqrt {n})!$ when $n \rightarrow \infty$?

Published on 25 Oct 2018 - 3:40

score 93 · Answer 6 · 2018-10-25 16:01:11

93

Views

Calculate $\lim_{k \to \infty}(1+2^{k+1})^{(2^{k-2})-2}\cdot\frac{(2^k-1)^2}{(2^k-1)!!}$

Published on 25 Oct 2018 - 16:01

score 4.7k · Answer 7 · 2018-10-25 19:43:13

4.7k

Views

Limit with factorial (Stolz & Stirling)

Published on 25 Oct 2018 - 19:43

score 126 · Answer 8 · 2026-03-21 18:54:14

126

Views

Still unclear why Hanson's proof that $\text{lcm}(1,…,n)<3^n$ is not sufficient to resolve Legendre's Conjecture.

Published on 21 Mar 2026 - 18:54

score 51 · Answer 9 · 2018-10-26 02:59:56

51

Views

$f(x)= x^2 -6x -9$ and $f(p)=f(-q)$. Find $p-q$

Published on 26 Oct 2018 - 2:59

score 620 · Answer 10 · 2018-10-26 06:04:16

620

Views

On the relationship between exponents and factorials

Published on 26 Oct 2018 - 6:04

score 78 · Answer 11 · 2018-10-27 16:10:48

78

Views

Two variable Factorial Conjecture needing direct proof

Published on 27 Oct 2018 - 16:10

score 152 · Answer 12 · 2018-10-28 00:10:45

152

Views

Asymptotic behavior of a certain function

Published on 28 Oct 2018 - 0:10

score 147 · Answer 13 · 2018-10-28 16:50:47

147

Views

Stirling numbers of the second kind - proof 2

Published on 28 Oct 2018 - 16:50

score 80 · Answer 14 · 2018-10-28 19:40:24

80

Views

For part b) below, is the probability equal to (1/6+1/6-1/36), or (1/6+1/6-1/30)?

Published on 28 Oct 2018 - 19:40

score 167 · Answer 15 · 2018-10-29 11:42:04

167

Views

Formal proof of the sequence involving double factorials $x_n = \frac{(2n)!!}{(2n-1)!!}$ is not bounded.

Published on 29 Oct 2018 - 11:42

List Question

Does a factorial always differ by a square from a square?

Closed form for a sum

Limit of $\frac{N^{n}(N!)^{n}}{(n-1)!}$ as $n$ tends to infinity

Trying to prove : $n! ≥ (n/2)^{n/2}$

Which grows at a faster rate $\sqrt {n!}$ vs $(\sqrt {n})!$ when $n \rightarrow \infty$?

Calculate $\lim_{k \to \infty}(1+2^{k+1})^{(2^{k-2})-2}\cdot\frac{(2^k-1)^2}{(2^k-1)!!}$

Limit with factorial (Stolz & Stirling)

Still unclear why Hanson's proof that $\text{lcm}(1,…,n)<3^n$ is not sufficient to resolve Legendre's Conjecture.

$f(x)= x^2 -6x -9$ and $f(p)=f(-q)$. Find $p-q$

On the relationship between exponents and factorials

Two variable Factorial Conjecture needing direct proof

Asymptotic behavior of a certain function

Stirling numbers of the second kind - proof 2

For part b) below, is the probability equal to (1/6+1/6-1/36), or (1/6+1/6-1/30)?

Formal proof of the sequence involving double factorials $x_n = \frac{(2n)!!}{(2n-1)!!}$ is not bounded.

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