[seqfan] Re: A236767

[Allan Wechsler]

Hans, how did you notice the correspondence with A089001? Is this the sort
of thing Superseeker finds?


On Fri, Jan 31, 2014 at 11:05 AM, David Applegate <david at research.att.com>wrote:

> Yes.  If x^2 = y^4 + p, let a = x - y^2.  Then
>
> y^4 + p = x^2 = (y^2 + a)^2 = y^4 + 2 a y^2 + a^2
>
> so
>
> p = 2 a y^2 + a^2, and so a divides p.  Since p is a prime, a must be
> a unit (that is, +1 or -1).
>
> But since p >= 2, a must be +1.
>
> -Dave
>
> > From seqfan-bounces at list.seqfan.eu Fri Jan 31 10:48:46 2014
> > From: Hans Havermann <gladhobo at teksavvy.com>
> > Date: Fri, 31 Jan 2014 10:48:28 -0500
> > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > Subject: [seqfan] A236767
>
> > I'm currently contributing/editing this new sequence: 2, 10, 37, 82,
> 442, 577, ..., numbers whose square is a fourth power plus a prime. After a
> day of working on a b-file, I noticed that - up to the number of terms that
> I had calculated (just short of 500) - this sequence matched A089001^2 + 1.
> It's easy to show that A089001^2 + 1 will always be a member but are they
> the *only* members?
>
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