Timeline for Density of multi-grade solutions to $x_1^k+x_2^k+x_3^k = y_1^k+y_2^k+y_3^k$ for $k = 5$ or $6$?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Jan 4, 2015 at 16:59 | comment | added | Wolfgang | Yes, I fully agree :( Thank you that the caution didn't prevent you from posting your question! | |
| Jan 4, 2015 at 16:38 | comment | added | Tito Piezas III | Thanks for the graphs. But one can always use Skewes' number as a cautionary tale. The smallest known crossing is $\approx e^{728}$. On the other hand, the Birch and Swinnerton-Dyer conjecture in the 1960s initially used rather tenuous trends in graphical plots. Supposedly this made Birch's Ph.D. advisor J. Cassels skeptical, but over time the numerical evidence stacked up. So in the absence of anything definite, it shouldn't hurt to look at more data, especially for $k=6$. | |
| Jan 4, 2015 at 16:00 | history | answered | Wolfgang | CC BY-SA 3.0 |