Timeline for Are there arbitrarily long arithmetic progressions in every increasing sequence of positive integers with bounded gaps between consecutive terms?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Oct 4, 2021 at 14:13 | vote | accept | Kai Wang | ||
| Oct 1, 2021 at 20:22 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| Oct 1, 2021 at 19:47 | comment | added | GH from MO | Let $S$ be the OP's set. I think we can simply define the color of a positive integer $n$ as $\min\{i\geq 1:n+i\in S\}$. By assumption, the color of each $n$ is bounded by $T$, so we used finitely many colors. By van der Waerden's theorem, there is an arbitrary long arithmetic progression $P$ which is monochromatic. If the color of $P$ is $i$, then $P+i$ is a long arithmetic progression in $S$. | |
| Oct 1, 2021 at 19:36 | history | answered | Fedor Petrov | CC BY-SA 4.0 |