List questions from factorial

Published on 27 Mar 2026 - 14:55

157

Views

How to show using proof by induction: $\sqrt[n]{n!} \leqslant \frac{n+1}{2}, n \in \mathbb{Z}^+$

Published on 10 Apr 2016 - 19:57

87

Views

Proof by mathematical induction that $2^n < (n+2)!$ for all $n\ge 0$

Published on 11 Apr 2016 - 8:11

218

Views

Prove that $n! = O(n^n)$

Published on 11 Apr 2016 - 23:05

1.1k

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Congruence Modulo involving factorials

Published on 31 Mar 2026 - 19:11

1k

Views

Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

Published on 12 Apr 2016 - 23:32

622

Views

Divisibility via Induction: $8^n\mid (4n)!$

Published on 13 Apr 2016 - 7:24

487

Views

An inequality with exponents, factorials and nth roots!

Published on 14 Apr 2016 - 10:50

182

Views

Combinations equation solving with factorial

Published on 14 Apr 2016 - 22:34

753

Views

The exponent of $11$ in the prime factorization of $ 300!$ is___.

Published on 16 Apr 2016 - 12:28

468

Views

What does an exclamation point raised to a power, with no preceding number, mean?

Published on 17 Apr 2016 - 16:57

888

Views

Big O for factorials

Published on 05 Apr 2026 - 12:45

78

Views

$n!>a$, can we solve for $n$ in terms of $a$?

Published on 18 Apr 2016 - 1:24

4.3k

Views

Does (9/2)! have a real answer or not?

Published on 18 Apr 2016 - 17:37

315

Views

If $x+y+z=3k$, where $x, y, z, k$ are integers, prove that $x!y!z! \geq (k!)^3$

Published on 19 Apr 2016 - 15:25

List Question

Majoration of the $p$-adic valuation of a factorial.

How to show using proof by induction: $\sqrt[n]{n!} \leqslant \frac{n+1}{2}, n \in \mathbb{Z}^+$

Proof by mathematical induction that $2^n < (n+2)!$ for all $n\ge 0$

Prove that $n! = O(n^n)$

Congruence Modulo involving factorials

Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$

Divisibility via Induction: $8^n\mid (4n)!$

An inequality with exponents, factorials and nth roots!

Combinations equation solving with factorial

The exponent of $11$ in the prime factorization of $ 300!$ is___.

What does an exclamation point raised to a power, with no preceding number, mean?

Big O for factorials

$n!>a$, can we solve for $n$ in terms of $a$?

Does (9/2)! have a real answer or not?

If $x+y+z=3k$, where $x, y, z, k$ are integers, prove that $x!y!z! \geq (k!)^3$

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