Timeline for Find the diophantine-equations $3x(x^2+2)=y^2$ integer solution [closed]
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| S Mar 11, 2017 at 10:29 | history | unlocked | CommunityBot | ||
| S Mar 11, 2017 at 10:29 | history | locked | CommunityBot | ||
| S Mar 11, 2017 at 10:29 | history | closed |
Will Jagy R.P. Felipe Voloch Marco Golla Alexey Ustinov |
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| Mar 11, 2017 at 1:39 | answer | added | Favst | timeline score: 4 | |
| Mar 11, 2017 at 1:04 | comment | added | Igor Rivin | Whereup Magma says: > IntegralPoints(E); [ (0 : 0 : 1), (3 : -9 : 1), (6 : 18 : 1), (72 : -612 : 1) ] [ <(0 : 0 : 1), 1>, <(3 : -9 : 1), 1>, <(6 : 18 : 1), 1>, <(72 : -612 : 1), 1> ] | |
| Mar 11, 2017 at 1:02 | comment | added | Igor Rivin | @JeremyRouse You get $X((X/3)^2+2) = Y^2,$ So setting $\mathfrak{Y} = 3 Y,$ we finally get $X^3 + 18 X = \mathfrak{Y}^2.$ | |
| Mar 11, 2017 at 0:47 | comment | added | Jeremy Rouse | You can multiply both sides by $9$. Then set $X = 3x$ and $Y = 3y$ and get $Y^2 = f(X)$, where $f$ is monic. | |
| Mar 11, 2017 at 0:32 | comment | added | Igor Rivin | @JoeSilverman True, but most software (Magma, Sage), likes $y^2 = f(x),$ where $f(x)$ is a monic polynomial. If you would tell the OP how to transform his question to that form, I am sure s/he would be delighted. | |
| Mar 11, 2017 at 0:23 | history | edited | Fan Zheng |
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| Mar 11, 2017 at 0:18 | comment | added | Joe Silverman | There's a vast literature on finding integer points on elliptic curves. It's very likely that this curve has been analyzed, although I don't know a reference offhand. In any case, you should add tags for nt.number-theory and for elliptic-curve. | |
| Mar 11, 2017 at 0:06 | review | Close votes | |||
| Mar 11, 2017 at 10:29 | |||||
| Mar 10, 2017 at 23:34 | history | asked | math110 | CC BY-SA 3.0 |