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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• References: <20130203074843.D429168B0@smc.vnet.net>

```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
>

```

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