Timeline for On the equations $(x^n+1)(y^n+1)=z^2+1$ and $(x^n-1)(y^n-1)=z^2+1$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 12, 2021 at 9:42 | comment | added | Zhi-Wei Sun | Now I guess that the equation $(x^k+1)(y^m+1)=z^n+1$ with $x,y,z\in\{1,2,3,\ldots\}$, $k,m,n\in\{3,4,5,\ldots\}$ and $k\ge m$ has a unique solution: $(3^5+1)(12^3+1)=75^3+1$. | |
| May 12, 2021 at 7:13 | comment | added | Zhi-Wei Sun | I find that $(3^5+1)(12^3+1)=75^3+1$, | |
| May 12, 2021 at 7:02 | comment | added | Zhi-Wei Sun | I also conjecture that for each $n=3,4,5,\ldots$ the equation $(x^n+1)(y^n+1)=z^n+1$ has no positive integer solution. | |
| May 12, 2021 at 5:40 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |