Timeline for Special Case of famous Equation
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 29, 2013 at 22:15 | vote | accept | user44801 | ||
| Dec 29, 2013 at 21:36 | comment | added | user44801 | Ok, I appreciate your advice sir. | |
| Dec 29, 2013 at 17:04 | answer | added | Siksek | timeline score: 6 | |
| Dec 29, 2013 at 16:56 | comment | added | Joe Silverman | When writing something mathematical, it's always best to be precise, since the reader may not be able to guess what you mean. So if you mean "no non-trivial solutions", then that's what you should write. (I hope that you will take this as the constructive criticism that it's meant to be. I'm paraphrasing advice that I give to my PhD students; that they should always proofread what they've written as if they are someone seeing the material for the first time. So every statement needs to be precise.) | |
| Dec 29, 2013 at 16:07 | comment | added | user44801 | I was referring to non-trivial solutions. Besides $(n,y)=(1,±1)$ are always solutions of the Nagell-Ljunggren diophantine. | |
| Dec 29, 2013 at 15:53 | comment | added | Joe Silverman | First, you say that there are no solutions, but $(n,y)=(1,\pm1)$ are solutions. Second, did you try factoring $5^n=(2y)^2+1$ as $ (2+i)^n(2-i)^n = (2y+i)(2y-i)$? This might lead to an elementary proof (if you consider using the fact that $\mathbb{Z}[i]$ is a PID elementary). | |
| Dec 29, 2013 at 15:49 | review | First posts | |||
| Dec 29, 2013 at 16:06 | |||||
| Dec 29, 2013 at 15:30 | history | asked | user44801 | CC BY-SA 3.0 |