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Topic: Fibonacci integers
Replies: 2   Last Post: Feb 3, 2013 8:20 PM

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Bob Hanlon

Posts: 906
Registered: 10/29/11
Re: Fibonacci integers
Posted: Feb 3, 2013 8:20 PM
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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@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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