User Mark Fischler

50 votes

2 answers

2k views

Prove that $\sum_{n=1}^\infty \frac{n!}{n^n}$is irrational.

asked Mar 11, 2015 at 20:42

17 votes

6 answers

612 views

Near-Pythagorean triplets: What are the general solutions to $a^2+b^2=c^2-1$?

asked Aug 10, 2021 at 15:53

14 votes

1 answer

571 views

If $a+b+c = 3abc$ and $\frac17 \leq k \leq 7$ prove $ \frac1{ka+b}+\frac1{kb+c}+\frac1{kc+a} \leq \frac3{k+1} $

asked Mar 22, 2017 at 21:25

12 votes

1 answer

1k views

Number of distinct angles that can be formed on a square grid

asked Nov 21, 2014 at 0:52

11 votes

3 answers

618 views

Is there a clean non-contrived theorem that can only be proven by contradiction?

asked Jul 7, 2016 at 23:58

10 votes

3 answers

438 views

Limits of functions that can't be attacked by Taylor series or L'hopital's rule

asked Sep 12, 2016 at 21:31

10 votes

2 answers

1k views

Meromorphic, analytic, holomorphic and all that

asked May 26, 2016 at 15:03

10 votes

2 answers

350 views

Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?

asked Jun 21, 2017 at 21:07

9 votes

2 answers

139 views

Is it well known that for the Pythagorean spiral, $\sum_1^\infty\frac1{a_n+1} = \frac12$?

asked Aug 29, 2017 at 21:18

9 votes

1 answer

519 views

Are all nimbers included in the surreals?

asked Mar 8, 2016 at 0:17

9 votes

1 answer

411 views

What is known about the counting function of Gaussian primes"

asked Mar 18, 2016 at 5:56

9 votes

4 answers

1k views

A fierce differential-delay equation: df/dx = f(f(x))

asked Jun 4, 2014 at 0:11

8 votes

2 answers

239 views

Show that for a given $s$ there are a finite number of Fibonacci number of form $n^2+s$

asked May 7, 2015 at 19:08

8 votes

0 answers

118 views

How far has a chasing wasp flown as her target walks around a square?

asked Feb 21, 2017 at 23:34

8 votes

4 answers

175 views

Prove closed form for $\sum_{n\in\Bbb N}\frac1{5n(5n-1)}$

asked Mar 11, 2019 at 17:08

7 votes

2 answers

104 views

Prove $\lim_{m\to\infty}\sum_{k=1}^m\frac{2^{-k}}{k} = \log 2$

asked Apr 2, 2018 at 16:22

7 votes

2 answers

446 views

Does choosing a counting function require the Axiom of Choice?

asked Aug 22, 2016 at 23:05

6 votes

2 answers

142 views

Calculate the non-server's advantage in a win-by-two game

asked Aug 23, 2016 at 19:52

6 votes

5 answers

1k views

Arranging the alternating harmonic series to sum to $\sqrt{2}$

asked Jan 23, 2016 at 16:49

6 votes

5 answers

1k views

Easier way to show $\cos(20^\circ)\cos(30^\circ)\cos(40^\circ)=\cos^2(10^\circ)\cos(50^\circ)$

asked Jun 7, 2016 at 21:46

6 votes

1 answer

157 views

Show $a+b+c = 3abc \implies \frac1{a+b}+\frac1{b+c}+\frac1{c+a} \leq \frac32$

asked Mar 27, 2017 at 22:34

6 votes

3 answers

324 views

Want less brutish proof: if $a+b+c=3abc$ then $\frac1a+\frac1b+\frac1c\geq 3$

asked Mar 28, 2017 at 20:38

6 votes

2 answers

230 views

Area of "polygon" inscribed in circle, whose side lengths form a geometric series

asked Nov 7, 2016 at 21:29

5 votes

1 answer

207 views

Do any (non-trivial) 2-chains of Pythagorean triplets exist?

asked Jun 20, 2018 at 19:37

5 votes

2 answers

10k views

Is $\sin z/z$ analytic at the origin?

asked May 27, 2016 at 17:33

5 votes

3 answers

174 views

Greater/lesser search with one false answer allowed

asked Feb 24, 2016 at 23:19

5 votes

1 answer

341 views

Prove the product of a polynomial function of the roots of another polynomial is an integer.

asked Sep 1, 2016 at 16:38

4 votes

0 answers

213 views

Generating uniformly distributed random elements of $SU(3)$

asked Aug 17, 2016 at 20:47

4 votes

2 answers

584 views

Gauss's thesis: Theory of equations or hypergeometric functions, or both?

asked Jul 19, 2016 at 16:12

4 votes

2 answers

131 views

Where, in geometry, is the notion of "path length of a curve" introduced?

asked Mar 22, 2016 at 20:50

Stack Exchange Network

128 Questions

Prove that $\sum_{n=1}^\infty \frac{n!}{n^n}$is irrational.

Near-Pythagorean triplets: What are the general solutions to $a^2+b^2=c^2-1$?

If $a+b+c = 3abc$ and $\frac17 \leq k \leq 7$ prove $ \frac1{ka+b}+\frac1{kb+c}+\frac1{kc+a} \leq \frac3{k+1} $

Number of distinct angles that can be formed on a square grid

Is there a clean non-contrived theorem that can only be proven by contradiction?

Limits of functions that can't be attacked by Taylor series or L'hopital's rule

Meromorphic, analytic, holomorphic and all that

Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?

Is it well known that for the Pythagorean spiral, $\sum_1^\infty\frac1{a_n+1} = \frac12$?

Are all nimbers included in the surreals?

What is known about the counting function of Gaussian primes"

A fierce differential-delay equation: df/dx = f(f(x))

Show that for a given $s$ there are a finite number of Fibonacci number of form $n^2+s$

How far has a chasing wasp flown as her target walks around a square?

Prove closed form for $\sum_{n\in\Bbb N}\frac1{5n(5n-1)}$

Prove $\lim_{m\to\infty}\sum_{k=1}^m\frac{2^{-k}}{k} = \log 2$

Does choosing a counting function require the Axiom of Choice?

Calculate the non-server's advantage in a win-by-two game

Arranging the alternating harmonic series to sum to $\sqrt{2}$

Easier way to show $\cos(20^\circ)\cos(30^\circ)\cos(40^\circ)=\cos^2(10^\circ)\cos(50^\circ)$

Show $a+b+c = 3abc \implies \frac1{a+b}+\frac1{b+c}+\frac1{c+a} \leq \frac32$

Want less brutish proof: if $a+b+c=3abc$ then $\frac1a+\frac1b+\frac1c\geq 3$

Area of "polygon" inscribed in circle, whose side lengths form a geometric series

Do any (non-trivial) 2-chains of Pythagorean triplets exist?

Is $\sin z/z$ analytic at the origin?

Greater/lesser search with one false answer allowed

Prove the product of a polynomial function of the roots of another polynomial is an integer.

Generating uniformly distributed random elements of $SU(3)$

Gauss's thesis: Theory of equations or hypergeometric functions, or both?

Where, in geometry, is the notion of "path length of a curve" introduced?