Re: is there exist 3-rd degree real polynomial contains all Fibonacci numbers?

Gerry Myerson a écrit :
In article <r90ag4pfkkghi5e9ehim5o9scvkv9qibvk@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:

On Fri, 24 Oct 2008 02:37:11 -0700 (PDT), Pawel_Iks
<pawel.labedzki@xxxxxxxxx> wrote:

I want to know if there exist such polynomial W(x)=a*x^3+b*x^2+c*c+d
with property: for all n there exist k, such that: W(k)=F_n, where F_n
- n-th Fibonacci number.

What about other degrees of W?
Why did you start with degree 3?

What about degree 2?

What about other sequences?
How about the sequence

S = {1, 2, 4, 8, 16, ...}

of powers of 2.

Does there exist a polynomial f in Z[x], with deg(f) > 1, such that S
is a subset of f(Z)?

I think there's a theorem to the effect that if f is as above then the biggest prime dividing f(n) goes to infinity with n.

f(x) - f(y) is divisible by x-y ; could this help?
.

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