Timeline for Jacobsthal function related to squares
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19 events
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| Jun 3 at 3:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Sep 16, 2021 at 20:19 | history | edited | José Hdz. Stgo. | CC BY-SA 4.0 |
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| Jan 7, 2014 at 23:52 | comment | added | Gerhard Paseman | @panoramix, sorry for the delay. "On the integers relatively prime...[long title] ... by Jacobsthal" in Math. Scand. (1962) pp 163-170, by Erd\H{o}s. You can find a copy online with not too hard a web search. I put up a preprint arxiv.org/abs/1311.5944 on ArXiv with a short reading list and bibliography, if you want to see some recent progress. I especially recommend Hagedorn's paper. Gerhard "Version Two Arriving Next Week" Paseman, 2014.01.07 | |
| Dec 31, 2013 at 20:29 | comment | added | Konstantinos Gaitanas | @GerhardPaseman Can you give a refference for Erdos's paper you mentioned? | |
| Dec 11, 2011 at 8:39 | comment | added | Fred Daniel Kline | Do we have to start with a given n? I have a function that when given m will create an n that will be prime to all a in those ranges. | |
| Nov 4, 2011 at 21:44 | history | edited | Charles | CC BY-SA 3.0 |
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| Jul 15, 2011 at 18:53 | comment | added | Gerhard Paseman | I would like to know the motivation for choosing squares. Is it an approach to study primes of the form $a^2+1$? Also, I should mention that I do not see a way to provide any tight bounds on $h(m)$ without making assumptions on $m$ like "Suppose every prime factor of $m$ has -3 as a nqr..." Gerhard "Ask Me About System Design" Paseman, 2011.07.15 | |
| Jul 15, 2011 at 7:25 | answer | added | Gerhard Paseman | timeline score: 1 | |
| Jul 14, 2011 at 18:38 | comment | added | Gerhard Paseman | Also, Erdos has for almost all n that j(n) is not far from a bound like log(n)log(log(n)) in a 1962 paper. You might review that paper to see how much carries over to your situation. Gerhard "Email Me About System Design" Paseman, 2011.07.14 | |
| Jul 14, 2011 at 15:56 | comment | added | Gerhard Paseman | There are still a lot of quadratiic residues for many numbers. My guess is that the upper bound will not drop significantly, and may not drop at all. The analysis becomes more challenging for me because the answer may depend on the multiplicity of prime factors in the number. If -1 is not a quadratic residue and there are about half as many qrs as nqrs less than n, then by symmetry I expect the upper bound to be the same. Even in the general case I expect there to be no provable decrease in the upper bound. Gerhard "Ask Me About Jacobsthal's Function" 2011.07.14 | |
| Jul 14, 2011 at 8:56 | history | asked | tobias | CC BY-SA 3.0 |