Timeline for Does there exist a non-square number which is the quadratic residue of every prime?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 2, 2013 at 2:10 | comment | added | Ian Agol | This is an instance of the Hasse-Minkowski principle, which, as pointed out in the answers, is a souped-up version of quadratic reciprocity (cf. Hilbert symbols). en.wikipedia.org/wiki/Hasse%E2%80%93Minkowski_theorem | |
| Sep 1, 2013 at 23:27 | history | edited | j.c. | CC BY-SA 3.0 |
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| Sep 1, 2013 at 19:24 | history | edited | user9072 |
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| Jul 8, 2013 at 8:54 | vote | accept | Paul | ||
| Jul 8, 2013 at 2:10 | comment | added | paul garrett | Following on @LaurentBerger's remark, we can observe that for $\alpha$ an algebraic integer generating an abelian but not-cyclic extension of $\mathbb Q$, the minimal polynomial of $\alpha$ over $\mathbb Q$ is reducible modulo every prime. The simplest case is $x^4+1$. | |
| Jul 5, 2013 at 6:51 | comment | added | Laurent Berger | On the other hand, 16 is an 8th power modulo every prime! | |
| Jul 5, 2013 at 5:38 | answer | added | Noam D. Elkies | timeline score: 28 | |
| Jul 5, 2013 at 4:52 | answer | added | Igor Rivin | timeline score: 4 | |
| Jul 5, 2013 at 4:44 | answer | added | Michael Zieve | timeline score: 10 | |
| Jul 5, 2013 at 4:31 | review | First posts | |||
| Jul 5, 2013 at 5:37 | |||||
| Jul 5, 2013 at 4:31 | answer | added | brando | timeline score: 5 | |
| Jul 5, 2013 at 4:12 | history | asked | Paul | CC BY-SA 3.0 |