Question

Is either $n! + 1$ or $n! - 1$ not prime for all $n$?

score 1.2k · Answer 1 · 2020-08-31 23:17:02

1.2k

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Is either $n! + 1$ or $n! - 1$ not prime for all $n$?

Published on 31 Aug 2020 - 23:17

score 371 · Answer 2 · 2020-09-01 09:28:12

371

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A sum of absolute values of binomial coefficients

Published on 01 Sep 2020 - 9:28

score 151 · Answer 3 · 2020-09-01 16:33:54

151

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Prove that $n$ and $n + k$ are both primes if and only if $(k!)^2[(n - 1)! + 1] + n(k! - 1)(k - 1)! \equiv 0 \mod n(n + k)$.

Published on 01 Sep 2020 - 16:33

score 77 · Answer 4 · 2020-09-02 08:33:42

77

Views

Is there a general way to find large enough $n \in \mathbb N$ such that for $k \in \mathbb N$: $n!>k^{n}$

Published on 02 Sep 2020 - 8:33

score 650 · Answer 5 · 2026-04-04 00:48:40

650

Views

How to solve $ \sum_{i=1}^{n} \left \lfloor{\log{i}}\right \rfloor $ for closed form

Published on 04 Apr 2026 - 0:48

score 370 · Answer 6 · 2020-09-05 14:26:36

370

Views

Find the number of trailing zeros of $ 100! - 101! + ... - 109! + 110!$

Published on 05 Sep 2020 - 14:26

score 80 · Answer 7 · 2020-09-07 18:39:25

80

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Is there another way to write the product $ 2^2\times 3^2\times 4^2\times 5^2\times 6^2\times \cdots =(n^2)!\;$?

Published on 07 Sep 2020 - 18:39

score 76 · Answer 8 · 2020-09-09 04:31:11

Prove that $\frac{2} {(0! + 1! + 2!)} + \frac{3}{( 1! + 2! + 3!)} + · · · + \frac{n} {(n − 2)! + (n − 1)! + n! )}= 1 − \frac{1}{n!}$

score 1k · Answer 9 · 2026-04-10 07:11:13

1k

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Factorial to exponential conversion

Published on 10 Apr 2026 - 7:11

score 218 · Answer 10 · 2026-04-10 08:14:31

218

Views

Division between factorials

Published on 10 Apr 2026 - 8:14

score 282 · Answer 11 · 2020-09-10 10:38:46

282

Views

Definition of a Factorial

Published on 10 Sep 2020 - 10:38

score 546 · Answer 12 · 2026-04-10 21:20:10

546

Views

Depleted batteries

Published on 10 Apr 2026 - 21:20

score 155 · Answer 13 · 2026-04-03 18:36:47

155

Views

perfect factors from the prime factorization of a large number

Published on 03 Apr 2026 - 18:36

score 188 · Answer 14 · 2020-09-13 23:03:25

188

Views

What is the value of $\int_0^{\infty}\frac{1}{x!}\,dx$

Published on 13 Sep 2020 - 23:03

score 75 · Answer 15 · 2026-04-11 17:52:49

75

Views

Can one simplify this expression involving products of binomial coefficients?

Published on 11 Apr 2026 - 17:52

List Question

Is either $n! + 1$ or $n! - 1$ not prime for all $n$?

A sum of absolute values of binomial coefficients

Prove that $n$ and $n + k$ are both primes if and only if $(k!)^2[(n - 1)! + 1] + n(k! - 1)(k - 1)! \equiv 0 \mod n(n + k)$.

Is there a general way to find large enough $n \in \mathbb N$ such that for $k \in \mathbb N$: $n!>k^{n}$

How to solve $ \sum_{i=1}^{n} \left \lfloor{\log{i}}\right \rfloor $ for closed form

Find the number of trailing zeros of $ 100! - 101! + ... - 109! + 110!$

Is there another way to write the product $ 2^2\times 3^2\times 4^2\times 5^2\times 6^2\times \cdots =(n^2)!\;$?

Prove that $\frac{2} {(0! + 1! + 2!)} + \frac{3}{( 1! + 2! + 3!)} + · · · + \frac{n} {(n − 2)! + (n − 1)! + n! )}= 1 − \frac{1}{n!}$

Factorial to exponential conversion

Division between factorials

Definition of a Factorial

Depleted batteries

perfect factors from the prime factorization of a large number

What is the value of $\int_0^{\infty}\frac{1}{x!}\,dx$

Can one simplify this expression involving products of binomial coefficients?

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