Timeline for Curves with infinitely many integral points consecutive Fibonacci numbers
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2013 at 15:27 | vote | accept | joro | ||
| Jan 2, 2013 at 12:54 | comment | added | Siksek | The infinite sequence of points $(F_{2^n},F_{2^n+1})$ is on many curves $F(x,y)=0$. But all these curves have infinitely many points in common with $x^2+xy-y^2+1=0$. So the polynomials $F(x,y)$ and $x^2+xy-y^2+1$ have a non-constant common factor. Thus $x^2+xy-y^2+1$ divides $F$. | |
| Jan 2, 2013 at 12:37 | comment | added | joro | Thank you. Why say $(F_{2^n},F_{2^n+1})$ are not on some third curve since there are two known curves? | |
| Jan 2, 2013 at 12:29 | history | answered | Siksek | CC BY-SA 3.0 |