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15
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Finding a positive lower bound of the sequence $\frac{\sqrt[n]{n!}}n$

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#sequences-and-series #inequality #factorial #radicals
77
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Why is $\frac{1}{x} \sum_{n=1}^x \ln (n) \sim \ln(x) - \gamma$

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#exponential-function #factorial
383
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Finding the missing digits of $23!$

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#elementary-number-theory #factorial #number-systems #decimal-expansion
2.2k
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Permutations excluding repeated characters

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#permutations #factorial
1.2k
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Prove by induction and recursion that $n!=n(n-1)(n-2)...(3)(2)(1). $

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#induction #factorial #recursion
3.3k
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Reason of dividing to n! ( repetition ) on Permutations with Repetitions

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#permutations #factorial
429
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Solve the factorial equation $x! = c$

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#factorial
1.6k
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Can 720! be written as the difference of two positive integer powers of 3?

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#elementary-number-theory #diophantine-equations #exponentiation #factorial
551
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Can Stirling's approximation be used to obtain lower and upper bound for $\pi(x)$?

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#prime-numbers #approximation #factorial
4k
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How do you simplify $n!-(n-1)!$

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#elementary-number-theory #factorial
50
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Find the natural number $n>2$ such that $\frac{n!}{(n-1)!} + \frac{n!}{3!(n-3)!} = 2\frac{n!}{2!(n-2)!}$

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#elementary-number-theory #factorial
104
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Find a convergent solution for $a$

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#convergence-divergence #complex-numbers #factorial
215
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Incompatible results with double factorial different definitions

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#definition #factorial
163
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Proving $n! = n \Rightarrow (n = 1 \quad or \quad n = 2)$

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#elementary-number-theory #factorial
2k
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Intermediate digits of 34!

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#elementary-number-theory #contest-math #factorial #number-systems #decimal-expansion

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