Timeline for Parametrizing the solutions to a diophantine equation of degree four
Current License: CC BY-SA 3.0
6 events
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| Oct 25, 2015 at 12:30 | history | migrated | to math.stackexchange.com | ||
| Oct 24, 2015 at 1:36 | comment | added | Joe Silverman | @user81854 I don't understand. The three-fold $x^4+y^4+z^4=t^4+g^4$ is in fact birational to $\mathbb P^3$, so it can be "parametrized" (although the parametrization is likely to be messy). But solutions to this equation will not give you solutions to your original equation $x^4+y^4+z^4=2t^4$ unless $t=g$, and I can pretty much guarantee that the parametrization of the 5-variable equation will not have $t=g$ in general. There's a big difference between a (smooth) quartic surface in $\mathbb P^3$ and a (smooth) quartic 3-fold in $\mathbb P^4$, both in their geometry and in their arithmetic. | |
| Oct 23, 2015 at 21:50 | comment | added | user81854 | Thank you jeq for your reply , but that one does not help me for my exercice, the condition a+b+c=0 is not good for my exercice.Monday I will try to find Gerardin and Ferrari in library , it is closed the week-end in Paris. | |
| Oct 23, 2015 at 20:52 | comment | added | user81854 | Thank you Joe Silverman . I found reference for parametric solutions Gerardin 1910, Ferrari 1913 intermédiaire des maths x^4+y^4+z^4=t^4+g^4 | |
| Oct 23, 2015 at 20:39 | history | edited | Joe Silverman | CC BY-SA 3.0 |
added 130 characters in body
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| Oct 23, 2015 at 20:32 | history | answered | Joe Silverman | CC BY-SA 3.0 |