Timeline for Density of "Fibonacci friends"
Current License: CC BY-SA 4.0
10 events
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| Jul 7, 2023 at 2:47 | comment | added | Richard Stanley | A slick way to see that infinitely Fibonacci numbers are divisible by $n$ is the following: we can run the Fibonacci recurrence backward to define $F_k$ for all $k\in\mathbb{Z}$. Clearly the Fibonacci number modulo $n$ are periodic since there are only finitely many values of $(F_i,F_{i+1})$ mod $n$. But $F_0=0$. | |
| Jul 6, 2023 at 20:11 | history | edited | Joseph Van Name | CC BY-SA 4.0 |
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| Jul 6, 2023 at 18:41 | comment | added | LSpice | Re, I think part of the fun of working with Fibonacci numbers is coming up with silly names. Paul Sally liked to talk about numbers satisfying the recurrence $T(n + 3) = T(n + 2) + T(n + 1) + T(n)$, I forget with what initial condition, and called them, of course, Tribonacci numbers. | |
| Jul 6, 2023 at 16:26 | comment | added | Joseph Van Name | @bof. I just could not resist using the phrase 'Foobonacci sequence'. | |
| Jul 6, 2023 at 16:21 | history | edited | Joseph Van Name | CC BY-SA 4.0 |
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| Jul 6, 2023 at 6:16 | vote | accept | Dominic van der Zypen | ||
| Jul 5, 2023 at 15:12 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 5, 2023 at 14:38 | history | edited | Joseph Van Name | CC BY-SA 4.0 |
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| Jul 5, 2023 at 14:27 | comment | added | Tom De Medts | See also en.wikipedia.org/wiki/Pisano_period for more information about the actual (smallest) value of $m$ as a function of $n$, i.e., the order of $L_n$ as an element of $\operatorname{GL}_2(\mathbb{Z}_n)$. | |
| Jul 5, 2023 at 14:21 | history | answered | Joseph Van Name | CC BY-SA 4.0 |