Timeline for Nontrivial question about Fibonacci numbers?
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Sep 12, 2016 at 18:28 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Sep 28, 2012 at 2:34 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Feb 19, 2012 at 0:05 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Nov 20, 2011 at 8:19 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Nov 22, 2010 at 21:44 | comment | added | darij grinberg | Sorry, I meant $\frac15\left(\left(\frac{a}{2}\right)^2\pm 1\right)$. | |
| Nov 22, 2010 at 21:42 | comment | added | darij grinberg | ... smaller by means of jumping from one rational solution to another via Vieta). | |
| Nov 22, 2010 at 21:42 | comment | added | darij grinberg | Seriously I only find (1) and (5) of any interest. The rest are basically negative results (including (2) which is equivalent to saying that no Fibonacci number beyound $3$ is a power of a prime $\equiv 3\pmod 4$) and not particularly exciting (though this does not mean their proofs are simple!). As for (1), this looks to me like a variation on the Pell theme: if $a$ is even, then we are talking about whether $\left(\frac{a}{2}\right)^2\pm 1$ is a perfect square, which is Pell. I assume that the general case is, similarly, a matter of "Vieta jumping" (inductively making the unknowns ... | |
| Nov 22, 2010 at 20:30 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Nov 22, 2010 at 20:14 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Nov 21, 2010 at 4:25 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Nov 21, 2010 at 4:18 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Apr 9, 2010 at 4:04 | comment | added | Pete L. Clark | These are very striking results. Already I find 1) very surprising! | |
| Feb 1, 2010 at 0:06 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Jan 17, 2010 at 1:06 | comment | added | Michael Lugo | An alternate proof of (3) probably follows from the asymptotic formula for $F<sub>n</sub>$; $F_m F_n$ is between $F_{m+n-2}$ and $F_{m+n-1}$. I have not worked out the details. | |
| Jan 17, 2010 at 0:08 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Jan 16, 2010 at 7:43 | history | edited | José Hdz. Stgo. | CC BY-SA 2.5 |
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| Jan 16, 2010 at 7:28 | history | answered | José Hdz. Stgo. | CC BY-SA 2.5 |