Question

Diophantine with factorials

score 138 · Answer 1 · 2026-04-10 17:04:43

138

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Diophantine with factorials

Published on 10 Apr 2026 - 17:04

score 186 · Answer 2 · 2026-04-08 17:01:42

186

Views

Application of Stirling's formula

Published on 08 Apr 2026 - 17:01

score 96 · Answer 3 · 2026-04-11 08:42:49

96

Views

Is there any known formula that gives the value of a factorial as a sum?

Published on 11 Apr 2026 - 8:42

score 116 · Answer 4 · 2026-04-02 09:42:11

116

Views

Is there any way to find the number of zeroes at the end of $n!$ for $n\ge5$?

Published on 02 Apr 2026 - 9:42

score 147 · Answer 5 · 2026-03-30 17:08:14

147

Views

Prove that $\varphi (v,\cdots, v)=\sum _{|\alpha |=k}\frac{k!}{\alpha !}v^\alpha \varphi^\alpha $

Published on 30 Mar 2026 - 17:08

score 263 · Answer 6 · 2026-04-12 16:48:39

263

Views

Area under inverse gamma function branch from minimum to 1. Equivalent to $1-\int\limits_0^1x! dx=.077254…$ in closed form.

Published on 12 Apr 2026 - 16:48

score 257 · Answer 7 · 2026-04-09 15:25:57

257

Views

Conditional expectation of a component in a multinomial distribution: understanding of complex calculations

Published on 09 Apr 2026 - 15:25

score 100 · Answer 8 · 2026-04-09 09:08:34

100

Views

Conjecture about prime factors of a special sum

Published on 09 Apr 2026 - 9:08

score 52 · Answer 9 · 2026-04-13 04:18:32

52

Views

Is the value of the sum squarefree for every $n\ne 27\ $?

Published on 13 Apr 2026 - 4:18

score 53 · Answer 10 · 2026-04-11 22:35:46

53

Views

Birthday problem but with $2^{128}$ different days in the year

Published on 11 Apr 2026 - 22:35

score 122 · Answer 11 · 2026-04-12 08:42:46

122

Views

Proof about the power series of reciprocal multifactorials $m_x(k)=\sum_{n=0}^\infty \frac{x^n}{n\underbrace{!\cdots!}_{\text{k times}}}$

Published on 12 Apr 2026 - 8:42

score 152 · Answer 12 · 2026-04-12 08:42:00

152

Views

If a different factorial function would've been defined, what would the graph of this function look like?

Published on 12 Apr 2026 - 8:42

score 300 · Answer 13 · 2026-04-05 17:34:30

300

Views

Yes, $0!=1$, but... by convention?

Published on 05 Apr 2026 - 17:34

score 123 · Answer 14 · 2026-04-12 16:55:06

123

Views

Using generating functions to solve the recurrence relation for factorials

Published on 12 Apr 2026 - 16:55

score 104 · Answer 15 · 2026-04-12 16:55:08

104

Views

Using Gosper's factorial approximation to determine the maximal $n$ in $n! = 2^p$

Published on 12 Apr 2026 - 16:55

List Question

Diophantine with factorials

Application of Stirling's formula

Is there any known formula that gives the value of a factorial as a sum?

Is there any way to find the number of zeroes at the end of $n!$ for $n\ge5$?

Prove that $\varphi (v,\cdots, v)=\sum _{|\alpha |=k}\frac{k!}{\alpha !}v^\alpha \varphi^\alpha $

Area under inverse gamma function branch from minimum to 1. Equivalent to $1-\int\limits_0^1x! dx=.077254…$ in closed form.

Conditional expectation of a component in a multinomial distribution: understanding of complex calculations

Conjecture about prime factors of a special sum

Is the value of the sum squarefree for every $n\ne 27\ $?

Birthday problem but with $2^{128}$ different days in the year

Proof about the power series of reciprocal multifactorials $m_x(k)=\sum_{n=0}^\infty \frac{x^n}{n\underbrace{!\cdots!}_{\text{k times}}}$

If a different factorial function would've been defined, what would the graph of this function look like?

Yes, $0!=1$, but... by convention?

Using generating functions to solve the recurrence relation for factorials

Using Gosper's factorial approximation to determine the maximal $n$ in $n! = 2^p$

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