Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

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)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• 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
>

• References:
  • Fibonacci integers
    • From: Andre Hautot <ahautot@ulg.ac.be>