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 109 · Answer 1 · 2026-02-23 05:47:44

109

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 23 Feb 2026 - 5:47

score 130 · Answer 2 · 2026-02-23 04:00:55

130

Views

An Exponential Diophantine Equation related to the Erdos Ternary Conjecture

Published on 23 Feb 2026 - 4:00

score 50 · Answer 3 · 2026-02-23 05:47:18

50

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 23 Feb 2026 - 5:47

score 204 · Answer 4 · 2026-02-23 05:43:43

204

Views

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

Published on 23 Feb 2026 - 5:43

score 129 · Answer 5 · 2026-02-23 05:45:38

129

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 23 Feb 2026 - 5:45

score 81 · Answer 6 · 2026-02-23 05:40:42

81

Views

On a weak polynomial version of Erdős conjecture

Published on 23 Feb 2026 - 5:40

score 173 · Answer 7 · 2026-02-23 05:42:36

173

Views

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

Published on 23 Feb 2026 - 5:42

score 21 · Answer 8 · 2026-02-23 05:42:11

21

Views

infinite binary sequences of a certain family

Published on 23 Feb 2026 - 5:42

score 38 · Answer 9 · 2026-02-23 05:37:51

38

Views

Large sets and Erdős-discrepancy

Published on 23 Feb 2026 - 5:37

score 35 · Answer 10 · 2026-02-23 05:47:43

35

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 23 Feb 2026 - 5:47

score 58 · Answer 11 · 2026-02-23 05:47:18

58

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 23 Feb 2026 - 5:47

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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