Timeline for Parametric solutions of Pell's equation
Current License: CC BY-SA 3.0
5 events
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| Feb 2, 2015 at 18:31 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Feb 2, 2015 at 18:01 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Feb 2, 2015 at 16:24 | comment | added | Leonardo | Exactly. Actually, the integer $r$ is equal to the order of the finite (cyclic) group $R^\times/\Bbb Z[\sqrt{n}]^\times$, where $R$ denotes the ring of integers of the quadratic field $\Bbb Q(\sqrt{n})$. In any case, for a given $n$, the degree of $P$ is bounded; it only remains to prove that this bound does not depend on $n$ (and, ideally, that it equals $3$). | |
| Feb 2, 2015 at 15:29 | comment | added | Stefan Kohl♦ | Interesting. -- Thank you! If one could show that, say, $r \leq 3$, would this imply that the degree of $P$ is at most $6$? | |
| Feb 2, 2015 at 14:51 | history | answered | Leonardo | CC BY-SA 3.0 |