[seqfan] Re: near multiples of squares in Fibonacci, Lucas, Pell, etc. numbers

Allan Wechsler acwacw at gmail.com
Wed Jun 5 03:16:49 CEST 2013


Are there _any_ quadratic polynomials that take on an infinite number of
Fibonacci values for integral argument?


On Tue, Jun 4, 2013 at 9:06 PM, Max Alekseyev <maxale at gmail.com> wrote:

> SeqFans,
>
> I've just published at arxiv a manuscript on finding integral points
> on biquadratic curves with application to finding terms of the form
> a*m^2 + b in Lucas sequences:
> http://arxiv.org/abs/1306.0883
> As an example I established that among Fibonacci numbers only 2 and 34
> are of the form 2m^2+2; only 1, 13, and 1597 are of the form m^2-3;
> and so on.
>
> I would appreciate any comments or suggestions.
>
> P.S. I'm going to present this result at CanaDAM 2013 conference next week.
>
> Regards,
> Max
>
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