List questions from factorial

Published on 09 Oct 2019 - 19:48

156

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Compute $\lim\limits_{x \to \infty} \frac{\ln (x!)}{x \ln (x)}$

Published on 11 Oct 2019 - 0:18

55

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Differentiating a function with a factorial

Published on 11 Oct 2019 - 15:57

33

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Why $(2n+2)! ≥ (n+2)! (n+2)^n$ is true?

Published on 12 Oct 2019 - 8:19

120

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Is $37!$ divisible by $19!\cdot20!$?

Published on 13 Oct 2019 - 19:29

710

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Proving $n! =\Gamma (n+1)$ by induction

Published on 15 Oct 2019 - 22:03

127

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The proof of $(n+1)!(n+2)!$ divides $(2n+2)!$ for any positive integer $n$

Published on 28 Mar 2026 - 5:22

33

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Sum over factorials, proof: $\forall_{n,j\in\mathbb{N}}:n=\left(2j+2n+1\right)\sum_{r=1}^{n}f\left(n,j,r\right)$

Published on 18 Oct 2019 - 9:34

17

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counting integers in modular function

Published on 16 Mar 2026 - 7:20

430

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If $P$ is an odd prime number such that $P=2k+1$, then prove $(k!)^2\equiv (-1)^{k+1} \mod P$

Published on 23 Oct 2019 - 23:17

49

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Can someone simplify this? It's a closed form for the approximation of $(\ln(2))!.$

Published on 24 Oct 2019 - 16:32

204

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In Pollard's p-1 how is M calculated?

Published on 28 Mar 2026 - 6:01

59

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How do I calculate this limit of factorial?

Published on 26 Oct 2019 - 16:01

337

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Power of prime in prime factorization of a factorial.

Published on 28 Mar 2026 - 5:22

2k

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Powerball Lottery - How Many Possible Sets

Published on 27 Mar 2026 - 0:57

List Question

How many permutations of $ABCDEFG$ contain $AB$ and $DC$?

Compute $\lim\limits_{x \to \infty} \frac{\ln (x!)}{x \ln (x)}$

Differentiating a function with a factorial

Why $(2n+2)! ≥ (n+2)! (n+2)^n$ is true?

Is $37!$ divisible by $19!\cdot20!$?

Proving $n! =\Gamma (n+1)$ by induction

The proof of $(n+1)!(n+2)!$ divides $(2n+2)!$ for any positive integer $n$

Sum over factorials, proof: $\forall_{n,j\in\mathbb{N}}:n=\left(2j+2n+1\right)\sum_{r=1}^{n}f\left(n,j,r\right)$

counting integers in modular function

If $P$ is an odd prime number such that $P=2k+1$, then prove $(k!)^2\equiv (-1)^{k+1} \mod P$

Can someone simplify this? It's a closed form for the approximation of $(\ln(2))!.$

In Pollard's p-1 how is M calculated?

How do I calculate this limit of factorial?

Power of prime in prime factorization of a factorial.

Powerball Lottery - How Many Possible Sets

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