User Benjamin L. Warren

11 votes

1 answer

540 views

Prove that $1$ is the sum of three tetrahedral numbers infinitely many different ways

asked Oct 7, 2021 at 1:32

7 votes

3 answers

2k views

Roots of this sextic

asked May 24, 2023 at 18:14

6 votes

2 answers

784 views

Roots of this equation in x

asked May 30, 2023 at 13:58

6 votes

1 answer

994 views

Solution to sixth order equation

asked Dec 12, 2021 at 18:16

5 votes

1 answer

788 views

Is there a reference for these types of cubic identities?

asked Mar 27, 2023 at 0:36

5 votes

1 answer

538 views

Twin circles in a quadrilateral

asked Aug 24 at 0:54

4 votes

2 answers

460 views

Solve this sextic

asked Jun 23, 2022 at 3:52

4 votes

1 answer

464 views

Division problem

asked Dec 11, 2022 at 2:06

4 votes

4 answers

474 views

A certain inequality involving square roots of polynomials

asked Nov 14 at 2:57

3 votes

1 answer

117 views

Point of concurrency of three circles which pass through vertices of a triangle and erected equilateral triangles

asked Aug 16 at 17:42

3 votes

1 answer

260 views

A polynomial as a quadratic residue mod a prime

asked Dec 13, 2022 at 16:50

3 votes

1 answer

253 views

Nagel line of a tetrahedron?

asked Jun 8 at 8:41

3 votes

1 answer

285 views

Name this kimberling center

asked Jul 2 at 6:19

3 votes

0 answers

114 views

generalization of these identities

asked Jul 24, 2023 at 6:59

2 votes

1 answer

196 views

Are there infinitely many primes that can be written as a sum of $k$ fibonacci numbers

asked Apr 30, 2023 at 22:44

2 votes

0 answers

137 views

Name of this geometric point? [closed]

asked Jun 21, 2023 at 12:24

2 votes

1 answer

148 views

Closed form of $ \sum_{k_{j-1}=0}^{k_j}....\sum_{k_1=0}^{k_2} \sum_{k=0}^{k_1} k^m $ as a polynomial in $k_j$?

asked Jun 16, 2021 at 23:21

2 votes

1 answer

345 views

Show that $\sum_{i=0}^{2k} [ {n\choose i+1} + (-1)^{i+1}{n+i+1\choose i+1} ] \sum_{j=0}^i {i\choose j}(-1)^j (i+1-j)^{2k} =0.$

asked Jun 20, 2021 at 1:04

2 votes

1 answer

761 views

Prove that $ \sum_{i=0}^{2k}( {n+R-1\choose R+i} + (-1)^{i+1}{ n+R+i\choose R+i } )\sum_{j=0}^i {i\choose j}(-1)^j(i+1-j)^{2k}=0 $

asked Jun 28, 2021 at 22:12

1 vote

1 answer

274 views

Prove there are infinitely many squares which are the sum of two tetrahedral numbers [closed]

asked Jan 7, 2022 at 3:50

1 vote

2 answers

401 views

Integral solutions of quadratic equation $5 X² − 14 X⁢Y + 5 ⁢Y² = n$

asked Oct 19, 2022 at 1:09

1 vote

1 answer

168 views

Prove $ \sum_{i=0}^{2a+1} {2a+1 \choose i} B_{2a+1-i} [ (n+1)^i+(-n)^i ] =0 $ for Bernoulli numbers $B_{n}$

asked Jun 4, 2021 at 17:07

1 vote

2 answers

368 views

Closed form of $ \sum_{i=1}^{n-k} {n-1-i\choose k-1}i^a + \sum_{i=1}^k {n-1-i\choose n-1-k}$

asked Jun 15, 2021 at 0:17

1 vote

0 answers

68 views

Name of the perspector of the orthic triangle and excentral triangle

asked Jul 2 at 7:56

1 vote

0 answers

162 views

A certain circle formed by perpendiculars

asked Sep 2 at 21:41

1 vote

1 answer

247 views

Modular arithmetic problem

asked Feb 21, 2022 at 17:15

0 votes

2 answers

178 views

Radical line of two ellipses

asked Jan 31 at 2:59

0 votes

0 answers

78 views

Coordinates of the centers of the insphere and circumsphere

asked Aug 12 at 1:38

0 votes

0 answers

104 views

sum and difference of four cubes times sum and difference of four cubes equals sum and difference of four cubes?

asked Apr 30, 2023 at 23:54

0 votes

1 answer

132 views

Name this geometric point?

asked Jul 28, 2023 at 5:23

Stack Exchange Network

38 Questions

Prove that $1$ is the sum of three tetrahedral numbers infinitely many different ways

Roots of this sextic

Roots of this equation in x

Solution to sixth order equation

Is there a reference for these types of cubic identities?

Twin circles in a quadrilateral

Solve this sextic

Division problem

A certain inequality involving square roots of polynomials

Point of concurrency of three circles which pass through vertices of a triangle and erected equilateral triangles

A polynomial as a quadratic residue mod a prime

Nagel line of a tetrahedron?

Name this kimberling center

generalization of these identities

Are there infinitely many primes that can be written as a sum of $k$ fibonacci numbers

Name of this geometric point? [closed]

Closed form of $ \sum_{k_{j-1}=0}^{k_j}....\sum_{k_1=0}^{k_2} \sum_{k=0}^{k_1} k^m $ as a polynomial in $k_j$?

Show that $\sum_{i=0}^{2k} [ {n\choose i+1} + (-1)^{i+1}{n+i+1\choose i+1} ] \sum_{j=0}^i {i\choose j}(-1)^j (i+1-j)^{2k} =0.$

Prove that $ \sum_{i=0}^{2k}( {n+R-1\choose R+i} + (-1)^{i+1}{ n+R+i\choose R+i } )\sum_{j=0}^i {i\choose j}(-1)^j(i+1-j)^{2k}=0 $

Prove there are infinitely many squares which are the sum of two tetrahedral numbers [closed]

Integral solutions of quadratic equation $5 X² − 14 X⁢Y + 5 ⁢Y² = n$

Prove $ \sum_{i=0}^{2a+1} {2a+1 \choose i} B_{2a+1-i} [ (n+1)^i+(-n)^i ] =0 $ for Bernoulli numbers $B_{n}$

Closed form of $ \sum_{i=1}^{n-k} {n-1-i\choose k-1}i^a + \sum_{i=1}^k {n-1-i\choose n-1-k}$

Name of the perspector of the orthic triangle and excentral triangle

A certain circle formed by perpendiculars

Modular arithmetic problem

Radical line of two ellipses

Coordinates of the centers of the insphere and circumsphere

sum and difference of four cubes times sum and difference of four cubes equals sum and difference of four cubes?

Name this geometric point?