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Prove $\sqrt{n!} \gt \frac{n}{2}$ $\forall$ $n \ge 1$

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#sequences-and-series #inequality #induction #factorial
2.1k
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role of nCr factorial in binomial expansion

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#factorial
264
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Showing $\gcd(n!i+1,n!j+1) = 1$ for $n \in \mathbb{N}$ if $i$ and $j$ are integers with $1\leq i < j \leq n$

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#elementary-number-theory #divisibility #factorial #gcd-and-lcm
87
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Solving a factorial equation

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#number-theory #factorial
98
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Gamma function and factorial

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#real-analysis #factorial #gamma-function
317
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How to simplify $\frac{(2K)!}{(K!)^2}$

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#factorial
294
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Prove $(m!)^3(n!)^4|(3m)!(4n)!$ for all positive integers $m,n$

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#elementary-number-theory #divisibility #factorial
43
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Prime Factorization of very big factorials

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#factorial #factoring #prime-factorization
52
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Logic behind $n\geq 4\epsilon$ if $n!$ ends in $\epsilon$ zeroes

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#combinatorics #factorial
171
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Information theoretic interpretation of Stirling's formula

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#factorial #information-theory
153
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formula for all possible enumerations of a set of distinct elements without any duplicate pairs, triples, quadruples, etc.

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#probability #combinatorics #permutations #combinations #factorial
1k
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Using combinatorial reasoning to show $n!=\binom{n}{0}D_n+\binom{n}{1}D_{n-1}+\dots+\binom{n}{n}D_0$

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#combinatorics #permutations #binomial-coefficients #factorial
276
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Prove that no number in this list is prime - Formatting a proof advice

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#elementary-number-theory #proof-writing #factorial
239
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Approximation of a factorial

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#reference-request #approximation #factorial #gamma-function
82
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Field Theory, Factor Ring, Polynomials

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#polynomials #field-theory #factorial

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