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15
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Closed form for $0^n0!+1^n1!+\cdots+k^nk!$

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#summation #factorial #closed-form
102
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How to show that $\sum _{i=1}^{\infty } \frac{i (i+1)!}{(2 i+1)\text{!!}}=2+\frac{\pi }{2}$?

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#sequences-and-series #factorial
91
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Closed form from recurrence

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#sequences-and-series #factorial #closed-form #stirling-numbers
40
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Reducing $\frac{B!(C-B)!}{A!(B-A)!}$ where $A \le B \lt C$

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#combinatorics #factorial
491
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How do I find all possible integer solutions for a product of two variables?

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#proof-verification #factorial #integers
47
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How is this expression for the factorial derived?

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#factorial
77
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What is the remainder when $1\times 1! + 2\times 2! + 3\times 3! +\ldots+ 11\times 11! + 3$ is divided by $12!$?

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#divisibility #factorial
187
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Divisibility Proof $8^n\mid(4n)!$

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#elementary-number-theory #induction #divisibility #factorial
61
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What is the general term of $\sum_{i=2}^{n/2} (n-i)!$?

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#summation #factorial
127
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Prove that $q^i \equiv 1 \pmod {n!}$ for all $q, n \in \mathbb{Z^+}$ where the prime factors of $q$ are greater than $n$

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#elementary-number-theory #modular-arithmetic #factorial
111
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Find all values of $n, m \in \mathbb{Z^+}$ where ${n \choose m}=1984$

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#elementary-number-theory #factorial
100
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By M.I prove that?

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#sequences-and-series #discrete-mathematics #induction #factorial #education
143
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How to apply induction to this formula?

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#summation #factorial
40
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How to check the convergence of $\sum_{n=1}^{\infty} \frac{n^{n/2}}{n!}$

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#sequences-and-series #discrete-mathematics #convergence-divergence #factorial
163
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Perfect square or cube

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#number-theory #factorial #square-numbers

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