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 56 · Answer 2 · 2023-02-05 20:55:01

56

Views

Let $\sigma$ be a permutation of $\mathbb{N}$. Show that there must be an A.P: $a,a+d,a+2d$ such that $\sigma(a)<\sigma(a+d)<\sigma(a+2d).$

Published on 05 Feb 2023 - 20:55

score 53 · Answer 3 · 2023-02-10 19:49:59

53

Views

Prove that $ a, b, c $ are in arithmetic sequence for the given condition.

Published on 10 Feb 2023 - 19:49

score 113 · Answer 4 · 2023-02-13 11:40:01

113

Views

How many terms of the series $-12,-9,-6\ldots$ must be taken so that the sum may be $54$?

Published on 13 Feb 2023 - 11:40

score 51 · Answer 5 · 2023-02-22 17:25:40

51

Views

Sets of Consecutive primes that can be split in equal parts

Published on 22 Feb 2023 - 17:25

score 60 · Answer 6 · 2023-02-24 08:04:47

60

Views

Please review my proof of triangle existence

Published on 24 Feb 2023 - 8:04

score 87 · Answer 7 · 2026-03-25 17:22:46

87

Views

Equivalent formulations of finitistic Szemerédi's theorem

Published on 25 Mar 2026 - 17:22

score 54 · Answer 8 · 2026-02-23 09:34:28

54

Views

If $A\subset\mathbb{N}$ has A.P.'s of length $k$ for all $k\geq 1,$ then so does $\lceil cA\rceil := \{\lceil ca\rceil:a\in A\}$ for any real $c>0.$

Published on 23 Feb 2026 - 9:34

score 118 · Answer 9 · 2023-03-05 18:42:20

118

Views

If $A\subset\mathbb{N}$ has positive upper density, $B\subset\mathbb{N}$ is infinite, does $\exists c$ such that $\vert\{c+a:a\in A\}\cap B\vert>k?$

Published on 05 Mar 2023 - 18:42

score 106 · Answer 10 · 2026-03-26 13:01:22

106

Views

Determine $x,y\in\mathbb{R}$ such that $t^4-2xt^2+y^2=0$ has $4$ real solutions in an arithmetic progression

Published on 26 Mar 2026 - 13:01

score 23 · Answer 11 · 2026-03-27 06:15:18

23

Views

Arithmetic Progression/Sequence | Does it include terms prior to the initial term?

Published on 27 Mar 2026 - 6:15

score 142 · Answer 12 · 2026-03-26 21:09:22

142

Views

An arithmetic-progression-free subset with more than 256 elements of $\{0,1,2,...,3^8-1\}$

Published on 26 Mar 2026 - 21:09

score 49 · Answer 13 · 2026-03-26 11:05:09

49

Views

Prove that $0.\overline{123} = 0.123123123123...$ is rational

Published on 26 Mar 2026 - 11:05

score 232 · Answer 14 · 2023-04-01 16:42:00

232

Views

Find the number of distinct integers in the collection of first $500$ terms of each of the arithemetic progressions $\{1,4,...\}$ and $\{9,14,...\}$

Published on 01 Apr 2023 - 16:42

score 50 · Answer 15 · 2023-04-03 08:40:23

50

Views

mathematical expression for arithmetic sequence with 3 variables where 1 of them is known

Published on 03 Apr 2023 - 8:40

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?

Let $\sigma$ be a permutation of $\mathbb{N}$. Show that there must be an A.P: $a,a+d,a+2d$ such that $\sigma(a)<\sigma(a+d)<\sigma(a+2d).$

Prove that $ a, b, c $ are in arithmetic sequence for the given condition.

How many terms of the series $-12,-9,-6\ldots$ must be taken so that the sum may be $54$?

Sets of Consecutive primes that can be split in equal parts

Please review my proof of triangle existence

Equivalent formulations of finitistic Szemerédi's theorem

If $A\subset\mathbb{N}$ has A.P.'s of length $k$ for all $k\geq 1,$ then so does $\lceil cA\rceil := \{\lceil ca\rceil:a\in A\}$ for any real $c>0.$

If $A\subset\mathbb{N}$ has positive upper density, $B\subset\mathbb{N}$ is infinite, does $\exists c$ such that $\vert\{c+a:a\in A\}\cap B\vert>k?$

Determine $x,y\in\mathbb{R}$ such that $t^4-2xt^2+y^2=0$ has $4$ real solutions in an arithmetic progression

Arithmetic Progression/Sequence | Does it include terms prior to the initial term?

An arithmetic-progression-free subset with more than 256 elements of $\{0,1,2,...,3^8-1\}$

Prove that $0.\overline{123} = 0.123123123123...$ is rational

Find the number of distinct integers in the collection of first $500$ terms of each of the arithemetic progressions $\{1,4,...\}$ and $\{9,14,...\}$

mathematical expression for arithmetic sequence with 3 variables where 1 of them is known

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