Timeline for Rational points on the "quintic circle" $x^5 + y^5 = 7$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2015 at 18:16 | vote | accept | pre-kidney | ||
| Nov 22, 2015 at 11:59 | answer | added | Michael Stoll | timeline score: 41 | |
| Nov 22, 2015 at 11:58 | answer | added | Panurge | timeline score: 14 | |
| Nov 22, 2015 at 9:03 | comment | added | Daniel Loughran | The modular techniques and Frey curve machinery used to prove FLT could also possibly be made to apply in your case, but I am not an expert in these methods. | |
| Nov 22, 2015 at 8:58 | comment | added | Daniel Loughran | It helps to instead consider the corresponding projective curve $X^5 + Y^5 = 7Z^5$ in $\mathbb{P}^2$ of genus $6$. This has a rational point, namely $(X:Y:Z) = (1:-1:0)$. Your conjecture is that this is the only rational point. The similarity here to the $n=5$ case of Fermat's last theorem should be very clear. Of course the proof of FLT for all $n$ was very hard, however there exist elementary proofs for the $n=5$ case (en.wikipedia.org/wiki/…). Perhaps these could be adapted to your case. | |
| Nov 22, 2015 at 8:01 | history | edited | GH from MO |
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| Nov 22, 2015 at 7:43 | history | asked | pre-kidney | CC BY-SA 3.0 |