Question

Are there modular arguments for Legendre's conjecture?

score 108 · Answer 1 · 2026-03-25 16:13:31

108

Views

Are there modular arguments for Legendre's conjecture?

Published on 25 Mar 2026 - 16:13

score 32 · Answer 2 · 2023-11-26 20:39:50

32

Views

What is the change in angle of of a symmetric matrix when summed over a plane?

Published on 26 Nov 2023 - 20:39

score 654 · Answer 3 · 2026-02-23 12:06:37

654

Views

Conjecture: In Pascal's triangle with $n$ rows, the proportion of numbers less than the centre number approaches $e^{-1/\pi}$ as $n\to\infty$.

Published on 23 Feb 2026 - 12:06

score 398 · Answer 4 · 2023-11-28 08:22:42

398

Views

Can this be done? Split Pascal's triangle (without the $1$s) with a straight line into two regions of equal sums.

Published on 28 Nov 2023 - 8:22

score 89 · Answer 5 · 2023-11-28 23:33:07

89

Views

When does the magnitude of the gradient equal the surface area of the $dxdy$ patch?

Published on 28 Nov 2023 - 23:33

score 67 · Answer 6 · 2023-11-30 23:57:38

67

Views

An infinite linear system of equations with an uncountable number $A$ of equations

Published on 30 Nov 2023 - 23:57

score 40 · Answer 7 · 2023-12-01 06:32:01

40

Views

Are there some famous conjectures related to perfect graphs?

Published on 01 Dec 2023 - 6:32

score 137 · Answer 8 · 2023-12-01 15:20:08

137

Views

A question about a paper by Gilmer on union-closed sets conjecture

Published on 01 Dec 2023 - 15:20

score 407 · Answer 9 · 2023-12-02 10:32:07

407

Views

Take a random walk on Pascal's triangle, without revisits: Does the final number have infinite expectation?

Published on 02 Dec 2023 - 10:32

score 130 · Answer 10 · 2023-12-03 09:01:03

130

Views

Conjecture: $\prod\limits_{k=0}^{n}\binom{2n}{k}$ is divisible by $\prod\limits_{k=0}^n\binom{2k}{k}$ only if $n=1,2,5$.

Published on 03 Dec 2023 - 9:01

score 350 · Answer 11 · 2026-02-23 07:23:01

350

Views

Conjecture: If $\sum_{i=1}^n \frac{1}{x_i}=1$ then $x_i | x_j$

Published on 23 Feb 2026 - 7:23

score 98 · Answer 12 · 2023-12-08 06:20:11

98

Views

Does this recursive journey through Pascal's triangle always reach $1$?

Published on 08 Dec 2023 - 6:20

score 39 · Answer 13 · 2026-03-26 04:14:37

39

Views

A weaker version of the second Hardy-Littlewood conjecture.

Published on 26 Mar 2026 - 4:14

score 152 · Answer 14 · 2023-12-08 23:56:35

152

Views

A generalization of the Stolz-Cesàro: For $k\ge 1$, $\lim_{n\to\infty }\frac{a_{n+k}-a_n}{b_{n+k}-b_n}=l$ implies $\lim_{n\to\infty}\frac{a_n}{b_n}=l$

Published on 08 Dec 2023 - 23:56

score 1.3k · Answer 15 · 2023-12-15 08:32:58

1.3k

Views

Conjecture: $\sum\limits_{k=1}^nk^m=S_3(n)\times\frac{P_{m-3}(n)}{N_m}$ for odd $m>1 \ ;\ =S_2(n)\times\frac{P_{m-2}'(n)}{N_m}$ for even $m$.

Published on 15 Dec 2023 - 8:32

List Question

Are there modular arguments for Legendre's conjecture?

What is the change in angle of of a symmetric matrix when summed over a plane?

Conjecture: In Pascal's triangle with $n$ rows, the proportion of numbers less than the centre number approaches $e^{-1/\pi}$ as $n\to\infty$.

Can this be done? Split Pascal's triangle (without the $1$s) with a straight line into two regions of equal sums.

When does the magnitude of the gradient equal the surface area of the $dxdy$ patch?

An infinite linear system of equations with an uncountable number $A$ of equations

Are there some famous conjectures related to perfect graphs?

A question about a paper by Gilmer on union-closed sets conjecture

Take a random walk on Pascal's triangle, without revisits: Does the final number have infinite expectation?

Conjecture: $\prod\limits_{k=0}^{n}\binom{2n}{k}$ is divisible by $\prod\limits_{k=0}^n\binom{2k}{k}$ only if $n=1,2,5$.

Conjecture: If $\sum_{i=1}^n \frac{1}{x_i}=1$ then $x_i | x_j$

Does this recursive journey through Pascal's triangle always reach $1$?

A weaker version of the second Hardy-Littlewood conjecture.

A generalization of the Stolz-Cesàro: For $k\ge 1$, $\lim_{n\to\infty }\frac{a_{n+k}-a_n}{b_{n+k}-b_n}=l$ implies $\lim_{n\to\infty}\frac{a_n}{b_n}=l$

Conjecture: $\sum\limits_{k=1}^nk^m=S_3(n)\times\frac{P_{m-3}(n)}{N_m}$ for odd $m>1 \ ;\ =S_2(n)\times\frac{P_{m-2}'(n)}{N_m}$ for even $m$.

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