Timeline for On the diophantine equations $x^n+n=y^m$ and $x^n-n=y^m$
Current License: CC BY-SA 4.0
4 events
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| Jul 18, 2018 at 2:42 | comment | added | Zhi-Wei Sun | In the cited arXiv paper, I showed that for any integer $x > 1$, the sets $\{x^n+n:\ n=1,2,3,\ldots\}$ and $\{x^n-n:\ n=1,2,3,\ldots\}$ contain a complete system of residues modulo any positive integer. So I consider numbers of the form $x^n\pm n$ interesting and ask a question similar to Catalan's conjecture. | |
| Jul 17, 2018 at 7:50 | comment | added | Vesselin Dimitrov | Finiteness of solutions follows of course from the $abc$ conjecture. They look completely unassailable to me; Catalan is very special, and just changing the ``$1$'' to $2$ or $n$ or $m$ leads to equations apparently beyond all known techniques. | |
| Jul 17, 2018 at 5:12 | comment | added | Dmitry Vaintrob | Why do you think this diophantine equation is interesting? | |
| Jul 17, 2018 at 4:55 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |