Question

Finding maximum number of factors in n!

score 304 · Answer 1 · 2026-04-01 12:31:01

304

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Finding maximum number of factors in n!

Published on 01 Apr 2026 - 12:31

score 63 · Answer 2 · 2015-12-23 10:01:12

63

Views

Let $f(x) = x^n$. Show that $f^{(n)} = n!$ and $f^{(m)} (x) = 0$ for all $m > n$.

Published on 23 Dec 2015 - 10:01

score 626 · Answer 3 · 2015-12-23 11:43:50

626

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How to find the exponent of a prime in $n!$

Published on 23 Dec 2015 - 11:43

score 67 · Answer 4 · 2015-12-24 10:00:51

67

Views

Number of solution of $x\cdot (p-1)! \equiv x\pmod {np}$

Published on 24 Dec 2015 - 10:00

score 532 · Answer 5 · 2026-04-01 19:31:20

532

Views

Inequality proof involving multinomial coefficients

Published on 01 Apr 2026 - 19:31

score 194 · Answer 6 · 2015-12-28 11:58:28

194

Views

How to find 10th digit of $\sum_{k=1}^{49} k!$

Published on 28 Dec 2015 - 11:58

score 117 · Answer 7 · 2015-12-29 10:02:25

117

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Find $\lim\limits_{n \to \infty} \frac{1!+3!+\ldots+(2n-1)!}{2!+4!+\ldots+(2n)!}$

Published on 29 Dec 2015 - 10:02

score 201 · Answer 8 · 2015-12-29 13:42:40

201

Views

How to compute $\lim\limits_{x \to +\infty} \left(\frac{\left((x-1)^2-x\ln(x)\right)(x)!}{(x+2)!+7^x}\right)$?

Published on 29 Dec 2015 - 13:42

score 1.5k · Answer 9 · 2016-01-01 07:39:10

1.5k

Views

How to decide if a factorial is a multiple of certain number?

Published on 01 Jan 2016 - 7:39

score 1.6k · Answer 10 · 2016-01-02 00:54:37

1.6k

Views

Verify If Sum of Factorials is Divisible by Integer

Published on 02 Jan 2016 - 0:54

score 77 · Answer 11 · 2016-01-02 09:26:52

77

Views

Prove: $4^{2k+1}>1 \cdot 3 \cdot \dots \cdot (2k+1)$ where $k$ is a positive integer

Published on 02 Jan 2016 - 9:26

score 70 · Answer 12 · 2016-01-02 14:41:12

70

Views

Derivative of the function $(x)!$.

Published on 02 Jan 2016 - 14:41

score 1k · Answer 13 · 2016-01-02 16:59:08

1k

Views

Finding last two non-zero digits of 2016!

Published on 02 Jan 2016 - 16:59

score 348 · Answer 14 · 2016-01-03 16:37:13

348

Views

I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $

Published on 03 Jan 2016 - 16:37

score 948 · Answer 15 · 2016-01-04 10:14:54

948

Views

Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

Published on 04 Jan 2016 - 10:14

List Question

Finding maximum number of factors in n!

Let $f(x) = x^n$. Show that $f^{(n)} = n!$ and $f^{(m)} (x) = 0$ for all $m > n$.

How to find the exponent of a prime in $n!$

Number of solution of $x\cdot (p-1)! \equiv x\pmod {np}$

Inequality proof involving multinomial coefficients

How to find 10th digit of $\sum_{k=1}^{49} k!$

Find $\lim\limits_{n \to \infty} \frac{1!+3!+\ldots+(2n-1)!}{2!+4!+\ldots+(2n)!}$

How to compute $\lim\limits_{x \to +\infty} \left(\frac{\left((x-1)^2-x\ln(x)\right)(x)!}{(x+2)!+7^x}\right)$?

How to decide if a factorial is a multiple of certain number?

Verify If Sum of Factorials is Divisible by Integer

Prove: $4^{2k+1}>1 \cdot 3 \cdot \dots \cdot (2k+1)$ where $k$ is a positive integer

Derivative of the function $(x)!$.

Finding last two non-zero digits of 2016!

I need help to advance in the resolution of that limit: $ \lim_{n \to \infty}{\sqrt[n]{\frac{n!}{n^n}}} $

Which is larger, $\sqrt[2015]{2015!}$ or $\sqrt[2016]{2016!}$?

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