Timeline for Parametric solutions of Pell's equation
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| May 2, 2016 at 4:27 | history | edited | j.c. | CC BY-SA 3.0 |
better to link to the abstract page than the pdf directly
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| S May 2, 2016 at 4:23 | history | suggested | user57432 | CC BY-SA 3.0 |
link edited
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| May 2, 2016 at 4:15 | review | Suggested edits | |||
| S May 2, 2016 at 4:23 | |||||
| Feb 17, 2015 at 23:36 | vote | accept | Stefan Kohl♦ | ||
| Feb 17, 2015 at 23:36 | history | edited | Stefan Kohl♦ | CC BY-SA 3.0 |
Added a link to Leonardo's preprint.
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| Feb 15, 2015 at 20:26 | comment | added | Stefan Kohl♦ | Very nice -- thank you! -- A table of these polynomials for $n \leq 100$ can be found here. -- Though compare e.g. the polynomial $D = 821559147201x^2+14158405x+61$ you obtain for $n = 61$ with the one for the degree-6-solution ($100x^2-44x+5$) here ... . | |
| Feb 15, 2015 at 18:37 | comment | added | Leonardo | It can be proved that setting $P_1=P(c^{-1}X), Q_1=Q(c^{-1}X)$ and $D_1=D(c^{-1}X)$, with $c=\mbox{gcd}\left(b^3,(a+1)b,2(a+1)^2\right)$ we obtain the parametric solutions whose coefficients have the smallest absolute values (try for $n=31,a=1530$ and $b=273$). Indeed, given $n,a$ and $b$, all the parametric solutions (for $P$ of degree $2$) are given by $P_1(mX),Q_1(mX)$ and $D_1(mX)$, with $m\neq0$ integer. | |
| Feb 2, 2015 at 20:42 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Feb 2, 2015 at 14:55 | comment | added | Leonardo | Dear Stefan, I found a partial answer concerning the degree of $P$. In order to keep the above comments consistent, instead of editing my answer, I decided to write a new post. | |
| Jan 29, 2015 at 6:20 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Jan 28, 2015 at 1:40 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Jan 27, 2015 at 19:09 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Jan 27, 2015 at 18:15 | comment | added | Stefan Kohl♦ | A table of Leonardo's polynomials for $n \leq 100$ is available here. | |
| Jan 27, 2015 at 17:16 | comment | added | Stefan Kohl♦ | Great! -- Thank you! -- Can you also say something on whether there exist series where $P$ has degree larger than $6$, or whether the degree of $P$ is bounded at all? | |
| Jan 27, 2015 at 16:11 | history | edited | Leonardo | CC BY-SA 3.0 |
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| Jan 27, 2015 at 12:20 | history | answered | Leonardo | CC BY-SA 3.0 |