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How to complete this proof for Wilson's theorem

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#elementary-number-theory #prime-numbers #modular-arithmetic #factorial #congruences
272
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How to prove that $m!n!(m+n)!|(2m)!(2n)!$ for every pair of positive integers $(m,n)$?

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#elementary-number-theory #divisibility #factorial #ceiling-and-floor-functions
73
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Show that $n!\ge2^{\left(n-1\right)}\left(n-2\right)^2$ by using induction

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#inequality #induction #exponential-function #factorial
862
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Determine all pairs of positive integers $(m,n)$ that satisfies $m!+n!=m^n$

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#exponentiation #factorial
232
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Solving factorial inequality

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#inequality #induction #factorial
80
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Prove Combinatoric Inequality

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#combinatorics #discrete-mathematics #inequality #proof-writing #factorial
317
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A sum of series problem: $\frac{3}{1!+2!+3!} + \frac{4}{2!+3!+4!} + \cdots + \frac{2008}{2006!+2007!+2008!}$

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#summation #factorial
314
Views

An upper bound on the logarithm of factorial

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#inequality #logarithms #factorial
108
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Possible formula for $ f(x) = \sum_{n=0}^{\infty}x^{-n!} $

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#sequences-and-series #factorial
236
Views

Simplify $\frac{25!}{3!}$

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#combinatorics #factorial
291
Views

Difference Calculus of the Factorial Function for Negative Integer Powers of $x$

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#combinatorics #polynomials #recurrence-relations #factorial
440
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"Chain Rule" for Finite Difference Operator

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#combinatorics #polynomials #recurrence-relations #factorial
138
Views

Get a (continuous) approximation for the equipotential lines of the function $ f(L,\Delta)=2^{-L}\binom{L}{\frac{L-\Delta}{2}}$

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#binomial-coefficients #factorial #gamma-function
36
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Show $(n_{i}+g_{i}-1)!\simeq(g_{i}-1)! g_{i}^{n_{i}}$

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#calculus #sequences-and-series #factorial
82
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Evaluating a Difference Operator of a Product of Factorial Polynomials

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#combinatorics #proof-verification #polynomials #recurrence-relations #factorial

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