Re: Fibonacci integers
- To: mathgroup at smc.vnet.net
- Subject: [mg129680] Re: Fibonacci integers
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Sun, 3 Feb 2013 20:23:56 -0500 (EST)
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m = {{1, 1}, {1, 2}}; And @@ ( (MatrixPower[m, n] // Flatten) == ({{Fibonacci[2 n - 1], Fibonacci[2 n]}, {Fibonacci[2 n], Fibonacci[2 n + 1]}} // Flatten) // Thread) // FunctionExpand // FullSimplify[#, Element[n, Integers]] & True And @@ ( MapThread[ Equal, {MatrixPower[m, n], {{Fibonacci[2 n - 1], Fibonacci[2 n]}, {Fibonacci[2 n], Fibonacci[2 n + 1]}}}, 2] // FunctionExpand // FullSimplify[#, Element[n, Integers]] & // Flatten) True Bob Hanlon On Sun, Feb 3, 2013 at 2:48 AM, Andre Hautot <ahautot at ulg.ac.be> wrote: > > Hi, let > m={1,1},{1,2} > and n be an integer > > MatrixPower[m, n] = = {{Fibonacci[2 n - 1], Fibonacci[2 n]}, > {Fibonacci[2 n], Fibonacci[2 n + 1]}} > > should be indentically True > > I have tried FunctionExpand and FullSimplify without success, any idea ? > Thanks in advance, > > Andre >
- References:
- Fibonacci integers
- From: Andre Hautot <ahautot@ulg.ac.be>
- Fibonacci integers