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Find the remainder when $ 12!^{14!} +1 $ is divided by $13$

score 1.1k · Answer 1 · 2012-06-07 06:41:16

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Find the remainder when $ 12!^{14!} +1 $ is divided by $13$

Published on 07 Jun 2012 - 6:41

score 303 · Answer 2 · 2026-03-28 21:26:52

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The mathematics underlying this baroque expression of the double-factorial

Published on 28 Mar 2026 - 21:26

score 74 · Answer 3 · 2012-06-07 19:29:46

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$t > 2n^2 \implies t!>n^t$ for $n,t \in \mathbb{N}$

Published on 07 Jun 2012 - 19:29

score 9.2k · Answer 4 · 2012-06-08 12:29:19

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$m!n! < (m+n)!$ Proof?

Published on 08 Jun 2012 - 12:29

score 6.2k · Answer 5 · 2012-06-10 10:14:09

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Prove that $(p-1)! \equiv (p-1) \pmod{1+2+3+\cdots+(p-1)}$

Published on 10 Jun 2012 - 10:14

score 1.1k · Answer 6 · 2012-06-14 23:59:47

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Formula to calculate the number of possible positions for $x$ numbers

Published on 14 Jun 2012 - 23:59

score 483 · Answer 7 · 2012-06-15 15:32:51

483

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Summation of a factorial (total number terms in a polynomial)

Published on 15 Jun 2012 - 15:32

score 11.6k · Answer 8 · 2012-06-26 16:38:05

11.6k

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Given number of trailing zeros in n!, find out the possible values of n.

Published on 26 Jun 2012 - 16:38

score 30.1k · Answer 9 · 2012-06-27 19:39:48

30.1k

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Does the sequence $\frac{n!}{2^n}$ converge or diverge?

Published on 27 Jun 2012 - 19:39

score 425 · Answer 10 · 2012-06-27 23:44:48

425

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Does the series converge or diverge? $\sum_{n=1}^\infty\frac{4^n+n}{n!}$

Published on 27 Jun 2012 - 23:44

score 594 · Answer 11 · 2026-04-08 23:14:59

594

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How to approximate $\sum_{k=1}^n k!$ using Stirling's formula?

Published on 08 Apr 2026 - 23:14

score 10.4k · Answer 12 · 2012-06-29 15:57:56

10.4k

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Proof that $\frac{(2n)!}{2^n}$ is integer

Published on 29 Jun 2012 - 15:57

score 30.1k · Answer 13 · 2012-06-30 08:30:10

30.1k

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If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.

Published on 30 Jun 2012 - 8:30

score 519 · Answer 14 · 2012-07-01 17:28:38

519

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Does a closed form formula for the series ${n \choose n-1} + {n+1 \choose n-2} + {n+2 \choose n-3} + \cdots + {2n - 1 \choose 0}$ exist.

Published on 01 Jul 2012 - 17:28

score 419 · Answer 15 · 2026-04-08 19:07:13

419

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Limits defined for negative factorials (i.e. $(-n)!,\space n\in\mathbb{N}$)

Published on 08 Apr 2026 - 19:07

List Question

Find the remainder when $ 12!^{14!} +1 $ is divided by $13$

The mathematics underlying this baroque expression of the double-factorial

$t > 2n^2 \implies t!>n^t$ for $n,t \in \mathbb{N}$

$m!n! < (m+n)!$ Proof?

Prove that $(p-1)! \equiv (p-1) \pmod{1+2+3+\cdots+(p-1)}$

Formula to calculate the number of possible positions for $x$ numbers

Summation of a factorial (total number terms in a polynomial)

Given number of trailing zeros in n!, find out the possible values of n.

Does the sequence $\frac{n!}{2^n}$ converge or diverge?

Does the series converge or diverge? $\sum_{n=1}^\infty\frac{4^n+n}{n!}$

How to approximate $\sum_{k=1}^n k!$ using Stirling's formula?

Proof that $\frac{(2n)!}{2^n}$ is integer

If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.

Does a closed form formula for the series ${n \choose n-1} + {n+1 \choose n-2} + {n+2 \choose n-3} + \cdots + {2n - 1 \choose 0}$ exist.

Limits defined for negative factorials (i.e. $(-n)!,\space n\in\mathbb{N}$)

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