Question

Has it been proven that, if $\ y_n = x_{n+1} - x_n\ $ is non-decreasing, then $\ x_n\ $ cannot be a counter-example to Erdős Conjecture?

score 108 · Answer 1 · 2023-02-01 12:59:37

108

Views

Has it been proven that, if $\ y_n = x_{n+1} - x_n\ $ is non-decreasing, then $\ x_n\ $ cannot be a counter-example to Erdős Conjecture?

Published on 01 Feb 2023 - 12:59

score 129 · Answer 2 · 2023-03-19 15:10:22

129

Views

An Exponential Diophantine Equation related to the Erdos Ternary Conjecture

Published on 19 Mar 2023 - 15:10

score 49 · Answer 3 · 2023-05-18 17:40:05

49

Views

How to show $A_x:= \{ \left\lfloor x^n\right\rfloor:n\in\mathbb{N}\}$ is not an additive basis (of order $k=2$) of $\mathbb{N}$ if $x>1?$

Published on 18 May 2023 - 17:40

score 203 · Answer 4 · 2023-07-23 16:27:58

203

Views

Has this weak version of Erdős Conjecture on arithmetic progressions been proven, or is it still an open problem?

Published on 23 Jul 2023 - 16:27

score 128 · Answer 5 · 2023-07-26 14:18:39

128

Views

For every large set $A\subset \mathbb{N},$ there is a concave subsequence of $A$ of length $k$ for every $k\in\mathbb{N}$.

Published on 26 Jul 2023 - 14:18

score 80 · Answer 6 · 2023-09-13 16:18:36

80

Views

On a weak polynomial version of Erdős conjecture

Published on 13 Sep 2023 - 16:18

score 172 · Answer 7 · 2023-09-24 11:25:59

172

Views

Do large sets have this specific type of self-similarity?

Published on 24 Sep 2023 - 11:25

score 20 · Answer 8 · 2023-11-07 15:31:12

20

Views

infinite binary sequences of a certain family

Published on 07 Nov 2023 - 15:31

score 37 · Answer 9 · 2023-11-22 06:39:15

37

Views

Large sets and Erdős-discrepancy

Published on 22 Nov 2023 - 6:39

score 34 · Answer 10 · 2023-12-02 18:19:13

34

Views

If Erdős Conjecture on arithmetic progressions is true, and $A$ is large, then does there exist a consecutive A.P. of $A$ of length $k$ for every $k?$

Published on 02 Dec 2023 - 18:19

score 57 · Answer 11 · 2022-11-29 15:42:58

57

Views

Let $A_N$ be the subset of $\{1,\ldots,\ N\}$ that has no $3$-term A.P's and maximises $\sum_{n\in A_N}\frac{1}{n}.$ Does $A_N\to A003278?$

Published on 29 Nov 2022 - 15:42

List Question

Has it been proven that, if $\ y_n = x_{n+1} - x_n\ $ is non-decreasing, then $\ x_n\ $ cannot be a counter-example to Erdős Conjecture?

An Exponential Diophantine Equation related to the Erdos Ternary Conjecture

How to show $A_x:= \{ \left\lfloor x^n\right\rfloor:n\in\mathbb{N}\}$ is not an additive basis (of order $k=2$) of $\mathbb{N}$ if $x>1?$

Has this weak version of Erdős Conjecture on arithmetic progressions been proven, or is it still an open problem?

For every large set $A\subset \mathbb{N},$ there is a concave subsequence of $A$ of length $k$ for every $k\in\mathbb{N}$.

On a weak polynomial version of Erdős conjecture

Do large sets have this specific type of self-similarity?

infinite binary sequences of a certain family

Large sets and Erdős-discrepancy

If Erdős Conjecture on arithmetic progressions is true, and $A$ is large, then does there exist a consecutive A.P. of $A$ of length $k$ for every $k?$

Let $A_N$ be the subset of $\{1,\ldots,\ N\}$ that has no $3$-term A.P's and maximises $\sum_{n\in A_N}\frac{1}{n}.$ Does $A_N\to A003278?$

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