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How does $a^{a^n}$ compare with $n!$ asymptotically?

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#algorithms #asymptotics #exponentiation #factorial
147
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Four elevators stop on floors $1$ to $8$; a separate elevator stops on $1$ and $4$. Suppose you want to get from $1$ to $4$ ...

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#combinatorics #factorial
359
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$34!=295232799cd96041408476186096435ab000000$, find $a$ ,$b$, $c$, and $d$

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#elementary-number-theory #factorial
42
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Prove the given inequalities.

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#inequality #factorial
59
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How to prove this factorial equality

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#summation #factorial
288
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Solve $a!b!=a!+b!+c!$ where $a$, $b$ and $c$ are nonnegative integers.

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#number-theory #contest-math #diophantine-equations #factorial
780
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Probability of duplicated games in chess

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#probability #factorial
65
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Simplifying an alternating sum of a product of factorials

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#number-theory #summation #factorial #analytic-number-theory #gamma-function
331
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For What Non-Negative Integer Values of $n$ is $n!\geq 3^n$

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#proof-writing #numerical-methods #factorial
193
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Show that $(a!)^b b! \mid (ab)! $

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#elementary-number-theory #binomial-coefficients #divisibility #factorial
123
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What is longer? Length of $2^n$ or number of $0$ in $n!$?

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#number-theory #divisibility #factorial
123
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$n$-th derivative of $x^\alpha$ where $\alpha = m + 1/2$

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#derivatives #radicals #factorial #pochhammer-symbol
68
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Find the desired function or disprove its existence

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#polynomials #asymptotics #factorial #constraints #non-convex-optimization
49
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Showing that the number of queues is uniquely expresssed as the product of $2010$ positive integers.

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#combinatorics #contest-math #combinations #factorial
199
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Using Limits to extend the Factorials to Real numbers (and decimals)

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#limits #factorial #gamma-function

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