User Đào Thanh Oai - MathOverflow

18 votes

3 answers

1k views

An ellipse through 12 points related to Golden ratio

asked Jun 24, 2018 at 0:34

17 votes

2 answers

2k views

Is every odd positive integer of the form $P_{n+m}-P_n-P_m$?

asked Jun 28, 2018 at 10:58

15 votes

2 answers

2k views

Do two new special points in any triangle exist?

asked Sep 30, 2018 at 17:09

15 votes

2 answers

831 views

Can four integer numbers $x$, $y$, $x-y$, $x+y$ be powerful numbers where $\gcd(x,y)=1$?

asked Jul 3, 2024 at 2:43

13 votes

2 answers

2k views

Is it a new discovery on conic section?

asked May 8, 2021 at 12:14

11 votes

3 answers

987 views

An open triangle problem in plane geometry

asked Nov 14, 2021 at 11:50

10 votes

1 answer

2k views

Is new $n$-conjecture as follows correct?

asked Jul 7, 2020 at 7:38

10 votes

0 answers

5k views

Is the conjecture A+B=C following correct?

asked Jun 19, 2018 at 4:00

9 votes

2 answers

686 views

Strengthened version of Isoperimetric inequality with n-polygon

asked Apr 30, 2018 at 8:08

9 votes

2 answers

584 views

In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $

asked Jul 12, 2018 at 5:39

9 votes

0 answers

1k views

A new theorem (discovered in 2013) equivalent to Brianchon theorem (the old theorem) discovered in XIX century?

asked Jun 14, 2020 at 4:03

9 votes

1 answer

1k views

Possible new theorem in plane geometry encompassing 5 famous geometry theorems

asked Oct 24, 2020 at 3:31

8 votes

0 answers

618 views

Are there at least one of $a$, $b$, $c$, $a+b$, $b+c$, $c+a$ have h(P) $\le 3$? (was checked up to $10^{18}$)

asked Oct 3, 2019 at 14:58

8 votes

1 answer

615 views

A Muirhead Like Inequality

asked Jun 17, 2018 at 13:34

8 votes

2 answers

511 views

Can exist a positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ are not prime for all $n \ge 1$?

asked Jul 3, 2024 at 9:52

8 votes

1 answer

439 views

A Generalization of Andrica Conjecture

asked Jan 27 at 8:18

7 votes

4 answers

1k views

Let $X$ be a positive integer. Then $\pi{(X+\ln^2{X})}-\pi{(X-\ln^2{X})}>\ln{X}$?

asked May 2, 2024 at 3:24

7 votes

1 answer

730 views

Prove: If $P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

asked Jun 27, 2018 at 2:24

7 votes

1 answer

241 views

Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

asked Jul 11, 2018 at 9:39

7 votes

1 answer

783 views

A problem of four conics

asked Dec 12, 2018 at 15:36

6 votes

2 answers

525 views

An inequality related to area and sidelengths of a polygon $Area(A_1A_2....A_n) \le \frac{1}{n}cotg{\frac{\pi}{n}} \sum_{i=1}^nA_iA_{i+1}^2$

asked Jul 10, 2018 at 3:12

6 votes

2 answers

1k views

$\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

asked Jun 26, 2018 at 2:11

6 votes

1 answer

430 views

Like Bradley’s conjecture (Four incenters lie on a circle) [closed]

asked Jun 12, 2020 at 5:18

6 votes

1 answer

361 views

Is min exponents of three positive integers $n$, $n+1$ and $n+2$ $=1$ true or false?

asked Sep 22, 2019 at 6:26

6 votes

0 answers

347 views

Does this plane geometry theorem have a name (well-known)?

asked Feb 5, 2021 at 3:55

6 votes

2 answers

839 views

Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?

asked Jun 15, 2021 at 1:59

6 votes

1 answer

273 views

A Seven Circles Problem 2

asked Mar 5, 2025 at 9:19

6 votes

1 answer

309 views

Are the iterated centroids of a hexagon collinear with a distance ratio approaching $1/2$?

asked Jan 28 at 2:02

5 votes

1 answer

1k views

Is this a new result about hexagon?

asked Aug 29, 2024 at 9:20

5 votes

0 answers

159 views

A Seven Circles Problem

asked Mar 4, 2025 at 7:02

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129 Questions

An ellipse through 12 points related to Golden ratio

Is every odd positive integer of the form $P_{n+m}-P_n-P_m$?

Do two new special points in any triangle exist?

Can four integer numbers $x$, $y$, $x-y$, $x+y$ be powerful numbers where $\gcd(x,y)=1$?

Is it a new discovery on conic section?

An open triangle problem in plane geometry

Is new $n$-conjecture as follows correct?

Is the conjecture A+B=C following correct?

Strengthened version of Isoperimetric inequality with n-polygon

In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $

A new theorem (discovered in 2013) equivalent to Brianchon theorem (the old theorem) discovered in XIX century?

Possible new theorem in plane geometry encompassing 5 famous geometry theorems

Are there at least one of $a$, $b$, $c$, $a+b$, $b+c$, $c+a$ have h(P) $\le 3$? (was checked up to $10^{18}$)

A Muirhead Like Inequality

Can exist a positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ are not prime for all $n \ge 1$?

A Generalization of Andrica Conjecture

Let $X$ be a positive integer. Then $\pi{(X+\ln^2{X})}-\pi{(X-\ln^2{X})}>\ln{X}$?

Prove: If $P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

A problem of four conics

An inequality related to area and sidelengths of a polygon $Area(A_1A_2....A_n) \le \frac{1}{n}cotg{\frac{\pi}{n}} \sum_{i=1}^nA_iA_{i+1}^2$

$\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

Like Bradley’s conjecture (Four incenters lie on a circle) [closed]

Is min exponents of three positive integers $n$, $n+1$ and $n+2$ $=1$ true or false?

Does this plane geometry theorem have a name (well-known)?

Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?

A Seven Circles Problem 2

Are the iterated centroids of a hexagon collinear with a distance ratio approaching $1/2$?

Is this a new result about hexagon?

A Seven Circles Problem