Recurrent sequence/integral part/

flip2004

In the following $x_0$ and $x_1$ are integers and $A,B$ are given rational numbers. By [ X ] is denoted the integer part of $X$ . Suppose that
$x_{k+1}= \left[ Ax_k + Bx_{k-1} \right] \; ,\; \; k=1,2,...,n,... .$
It's possible to find $x_n$ as a function of variables $n,x_0 ,x_1,A,B$ ?

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Alex. Lupas

Valentin Vornicu

Is this an open problem?

**Posted:** Tue Aug 03, 2004 1:11 am

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We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.

Peter

I think flip meant Unsolved instead of Open?

Anyway I know there must be one for every value of A,B although I guess the general way of writing will be extremely complex...

Guess it'll start with:

...in the fibonacci sequence the n-th term is given by: $\displaystyle F(n)=\frac{(\frac{1+\sqrt{5}}2)^n-(\frac{1-\sqrt{5}}2)^n}{\sqrt{5}}$

and writing it as a lineary combination of fibonacci sequences.
Although I have to admit I didn't get it fixed myself yet.

**Posted:** Tue Aug 03, 2004 1:28 am

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Boo!

flip2004

I have'nt a solution of this problem.Regards,proposer.

**Posted:** Fri Aug 13, 2004 12:02 am

Valentin Vornicu

**Posted:** Fri Aug 13, 2004 3:37 am

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We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.

Peter

Valentin, this IS the open problems section Mr. Green

**Posted:** Fri Aug 13, 2004 5:23 am

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Boo!

Valentin Vornicu

**Posted:** Fri Aug 13, 2004 7:52 am

_________________
We all use math everyday: to forecast weather, to tell time, to handle money; we also use math to analyze crime, reveal patterns, predict behavior. Using numbers we can solve the biggest mysteries we know.

Peter

lol

well, he originally posted it in the open problems section, and you replied: "Is this an open question??"

And the times I replied were in open section as well Razz

(never even noticed it's been gone since then) Smile

**Posted:** Fri Aug 13, 2004 8:06 am

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Boo!