Timeline for Bound on the number of solutions of a specific Diophantine equation
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 30, 2014 at 18:21 | comment | added | Christopher D. Long | That should be Louis Marmet. My code combined with the various modular restrictions could easily extend the current bound. But the conjecture is almost certainly true - the "mixing" appears to be good enough that there could be nice asymptotics. | |
| Sep 28, 2014 at 13:51 | comment | added | Gerry Myerson | 1. I don't see any Mamet above, though I do see a Marmet below. 2. So does this mean you are able to extend the bounds reported some years ago? | |
| Sep 28, 2014 at 13:38 | comment | added | Christopher D. Long | There are some severe modulus restrictions on values of $n$ that could have unique solutions, so you only need to check a tiny fraction. Louis Mamet (mentioned above) discusses this in some detail. Also, once you find one additional solution beyond $\{2,n-2\}$ you can stop looking for more. | |
| Sep 27, 2014 at 23:52 | comment | added | Gerry Myerson | If it takes 10 seconds to find all solutions for $n=10^9$, then it would take something like $10^{11}$ seconds to find all solutions for all $n$, $1\le n\le10^{10}$. But comments elsewhere on the problem suggest that that calculation and more were done some years ago, so they must have had something much faster. | |
| Sep 27, 2014 at 18:04 | history | answered | Christopher D. Long | CC BY-SA 3.0 |