TheSimpliFire

Scotland

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PhD student and maths hobbyist interested in its wider applications.

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Can we remove any prime number with this strange process?

number-theory prime-numbers recreational-mathematics recursive-algorithms asked Jul 8, 2019 at 9:20

math.stackexchange.com

46 votes

How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$

real-analysis limits factorial closed-form gamma-function asked Feb 18, 2021 at 10:31

math.stackexchange.com

44 votes

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

integration special-functions power-towers asked Feb 15 at 17:52

math.stackexchange.com

36 votes

In molecular mechanics, how are van der Waals forces modelled?

molecular-dynamics intermolecular-forces molecular-mechanics interatomic-potentials asked Apr 28, 2020 at 19:45

mattermodeling.stackexchange.com

35 votes

Is $100$ the only square number of the form $a^b+b^a$?

number-theory modular-arithmetic square-numbers conjectures pythagorean-triples asked Jul 14, 2019 at 10:19

math.stackexchange.com

33 votes

Show that the maximum value of this nested radical is $\phi-1$

functions recursion maxima-minima nested-radicals golden-ratio asked Jan 5, 2019 at 16:41

math.stackexchange.com

29 votes

Sum of digits of $a^b$ equals $ab$

number-theory decimal-expansion conjectures asked Feb 24, 2019 at 17:10

math.stackexchange.com

27 votes

Is $\int_0^\infty{dx\over x^{x^{x^x}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^x}}}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^{x^{x^x}}}}}}}<\cdots$ true?

ca.classical-analysis-and-odes inequalities integration asked Feb 26 at 14:40

mathoverflow.net

27 votes

Show that $\left(\frac{x_1^{x_2}}{x_2}\right)^p+\left(\frac{x_2^{x_3}}{x_3}\right)^p+\cdots+\left(\frac{x_n^{x_1}}{x_1}\right)^p\ge n$ for any $p\ge1$

real-analysis inequality asked Oct 16, 2021 at 10:32

math.stackexchange.com

25 votes

Cubic programming and beyond?

reference-request nonlinear-programming asked Jul 11, 2019 at 18:41

or.stackexchange.com

Top Answers

Make 0 0 0 0 = 8

puzzling.stackexchange.com

Let $A=(a_{ij})$ be an $n\times n$ matrix. Suppose that $A^2$ is diagonal. Must $A$ be diagonal?

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Counter-intuitive results in OR

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Make 2019 with single digits

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Polyhedra, Polyhedron, Polytopes and Polygon

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Why is $\sum\limits_{n=1}^{\infty}e^{-(n/10)^2}$ almost equal to $5\sqrt\pi-\frac12$ (agreeing up to $427$ digits)?

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Some changes to the profile while we make it responsive

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Maximum value of $ab+bc+ca$ given that $a+2b+c=4$

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Does there exist a real function with domain $\Bbb{R}$ such that $f'(x)>0$ and $f''(x)+(f'(x))^2<0$ for all $x$?

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Is every $N$th Fibonacci number where $N$ is divisible by $5$ itself divisible by $5$

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Forced mate: 2 queens vs king

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Are there any "nonstandard" special angles for which trig functions yield radical expressions?

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Do they have to be integers?

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How to prove :$\sqrt{1!\sqrt{2!\sqrt{3!\sqrt{\cdots\sqrt{n!}}}}} <3$

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How are continued fractions related to quantum materials?

mattermodeling.stackexchange.com

Find $a$ and $b$ for which $\int_{0}^{1}( ax+b+\frac{1}{1+x^{2}} )^{2}\,dx$ takes its minimum possible value.

math.stackexchange.com

How to evaluate the limit of multifactorial $\lim_{n\to 0} \sqrt[n]{n!!!!\cdots !}$

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What is quadratization?

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How to map interval $[0, 100]$ to the interval $[100, 350]$?

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Can this determinant ever vanish?

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Use 2, 0, 1 and 8 to make 109

puzzling.stackexchange.com

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TheSimpliFire

Can we remove any prime number with this strange process?

How to evaluate double limit of multifactorial $\lim\limits_{k\to\infty}\lim\limits_{n\to 0} \sqrt[n]{n\underbrace{!!!!\cdots!}_{k\,\text{times}}}$

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

In molecular mechanics, how are van der Waals forces modelled?

Is $100$ the only square number of the form $a^b+b^a$?

Show that the maximum value of this nested radical is $\phi-1$

Sum of digits of $a^b$ equals $ab$

Is $\int_0^\infty{dx\over x^{x^{x^x}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^x}}}}}<\int_0^\infty{dx\over x^{x^{x^{x^{x^{x^{x^x}}}}}}}<\cdots$ true?

Show that $\left(\frac{x_1^{x_2}}{x_2}\right)^p+\left(\frac{x_2^{x_3}}{x_3}\right)^p+\cdots+\left(\frac{x_n^{x_1}}{x_1}\right)^p\ge n$ for any $p\ge1$

Cubic programming and beyond?