Timeline for Why certain diophantine equations are interesting (and others are not) ?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2013 at 21:36 | history | edited | Michael Hardy | CC BY-SA 3.0 |
added 10 characters in body
|
| Oct 18, 2010 at 6:27 | comment | added | Mike Bennett | And the particular example of a ``random'' Diophantine equation $$ x^3+y^5=z^2 $$ happens to be intimately connected to some of the most beautiful invariant theory of the 19th century due to Klein and others! It provides what is, in some sense, the most interesting example of a generalized Fermat equation in the so-called spherical case. Here, there are precisely $27$ parametrized families of coprime solutions, as shown in a very nice paper of Jonny Edwards in Crelle. | |
| Oct 17, 2010 at 1:28 | comment | added | JSE | And indeed, I'll add -- I never thought the generalized Fermat equations x^p + y^q = z^r were that interesting until I encountered the work of Henri Darmon explaining how these could be connected (at least in some cases) with natural families of abelian varieties with real multiplication over P^1 - 0,1,infty. Until then the problem seemed like a curiosity to me. | |
| Oct 16, 2010 at 21:27 | history | answered | JSE | CC BY-SA 2.5 |