Timeline for Squares in Lucas sequences
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2023 at 13:01 | answer | added | G. Melfi | timeline score: 2 | |
| Sep 9, 2020 at 9:54 | comment | added | Robert Frost | The main branch of the Collatz conjecture $1,5,21,85,\ldots=\frac{4^n-1}3$ is a Lucas sequence which factors into $\frac{(2^n-1)(2^n+1)}{3}$ and since these differ from a perfect square by $1$ I can't see this sequence containing many squares. | |
| Sep 26, 2019 at 16:11 | answer | added | John Machacek | timeline score: 7 | |
| Sep 26, 2019 at 7:42 | comment | added | Gerry Myerson | I don't know what you consider interesting. $2^n-1$ and $2^n+1$ are Lucas sequences with very easy proofs of rarity of squares. | |
| Sep 26, 2019 at 2:25 | comment | added | Max Alekseyev | You may like to check my paper On Integral Points on Biquadratic Curves and Near-Multiples of Squares in Lucas Sequences although it's more of computational rather than analytical nature. | |
| Sep 26, 2019 at 1:44 | history | edited | Jamai-Con | CC BY-SA 4.0 |
added 14 characters in body
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| Sep 26, 2019 at 1:21 | history | asked | Jamai-Con | CC BY-SA 4.0 |