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$\nu_3(n!)\simeq \nu_4(n!)$

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#number-theory #factorial #valuation-theory
193
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Formula related to combinatorial number

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#combinatorics #summation #binomial-coefficients #factorial
517
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Proof of $\int_0^1\ln\left(\frac{1}{\ln \frac{1}{x}}\right)dx=\gamma$

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#calculus #integration #definite-integrals #factorial #euler-mascheroni-constant
127
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Congruence modulo 7

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#elementary-number-theory #factorial
45
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Number of permutations increases $56$ times when number of elements increases by $2$, how many elements?

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#combinatorics #permutations #factorial
71
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Prove limit $\lim\limits_{n\to\infty} \frac{2^{2n+1} \cdot r^{2n} \pi^n \cdot n!}{(2n+1)!} = 0$

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#limits #factorial
45
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Computing $\frac{d^{n-1}}{dz^{n-1}}\frac{z}{\ln\left(z!\right)}^{n}$

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#calculus #derivatives #factorial #closed-form #gamma-function
393
Views

Why does 5000 factorial have 1249 trailing zeros and not 1248

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#elementary-number-theory #factorial #decimal-expansion
156
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Asymptotic behaviour of Gamma functions

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#numerical-methods #logarithms #asymptotics #factorial #gamma-function
131
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Do we have a simpler way to find all the positive integers satisfying $2^{n-1}|n!$?

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#number-theory #divisibility #factorial
140
Views

Exact fast factorial computation

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#abstract-algebra #polynomials #algorithms #factorial #integers
101
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Find the smallest $n$ for which $n!$ has more than $k$ digits for a given integer $k>0$

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#combinatorics #discrete-mathematics #factorial
544
Views

Closed form expression of $\Gamma(\frac{5}{3})$

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#calculus #integration #definite-integrals #factorial #gamma-function
61
Views

How can I have multiple combination restrictions?

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#combinatorics #factorial
119
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Using Stirling's Approximation to calculate how many ways to distribute certain objects among a group of children.

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#probability #probability-theory #statistics #probability-distributions #factorial

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