The Graham conjecture implies the Erdos-Turan conjecture
| dc.creator | Li, Liangpan | |
| dc.date | 2007-04-04 | |
| dc.date.accessioned | 2026-07-07T07:54:31Z | |
| dc.date.available | 2026-07-07T07:54:31Z | |
| dc.description | Erdös and Turán once conjectured that any set $A\subset\mathbb{N}$ with $\sum_{a\in A}{1}/{a}=\infty$ should contain infinitely many progressions of arbitrary length $k\geq3$. For the two-dimensional case Graham conjectured that if $B\subset \mathbb{N}\times\mathbb{N}$ satisfies $$\sum\limits_{(x,y)\in B}\frac{1}{x^2+y^2}=\infty,$$ then for any $s\geq2$, $B$ contains an $s\times s$ axes-parallel grid. In this paper it is shown that if the Graham conjecture is true for some $s\geq2$, then the Erdös-Turán conjecture is true for $k=2s-1$. | |
| dc.description | 3 pages | |
| dc.identifier | https://arxiv.org/abs/0704.0555 | |
| dc.identifier | http://arxiv.org/abs/0704.0555 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126640 | |
| dc.subject | Number Theory | |
| dc.subject | 11B25 | |
| dc.title | The Graham conjecture implies the Erdos-Turan conjecture | |
| dc.type | text |