Timeline for Number of integer solutions to a system of Diophantine inequalities
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2021 at 2:39 | comment | added | Tony419 | I see, I'll try this approach. Thanks a lot, Will! | |
| Feb 2, 2021 at 2:34 | comment | added | Will Sawin | The best approach might be to consider the real solution set, which I think is always the union of two regions, and use standard results to count lattice points in regions. In the limit as $a,b \to \infty$, unless $a,b$ are very close together, the functions $m^2+n^2$ and $m^3+n^3$ will behave approximately linearly near $a,b$ and these shapes will regions will converge to long, thin rectangles. A bound will then be the area of the rectangle or its diameter, whichever is larger. But getting explicit estimates might prove tricky... | |
| Feb 1, 2021 at 1:52 | history | asked | Tony419 | CC BY-SA 4.0 |