Next Problem

[Max Alekseyev]

On Dec 3, 2007 4:25 PM, Artur <grafix at csl.pl> wrote:
> P.S.
> Exactly "Don't existed such integer x,y that
> 1+2xy+x^2 y+y^2=0 "

Rewrite it as

y*(1+x)^2 = -y^2 + y - 1

Since the l.h.s. of this equality must be divisible by y, we have
either y=1 or y=-1. But neigther of these values corresponds to an
integer x.

Regards,
Max



I had some time today to continue the search:


possible dupes:
---------------

http://www.research.att.com/~njas/sequences/?q=id%3aA066023%7cid%3aA000578&p
=1&n=10&fmt=0
(aside from the first couple of terms, will these sequences ever differ?)

http://www.research.att.com/~njas/sequences/?q=id:A061557|id:A000782&fmt=0
(a couple of terms differ at the beginning)

http://www.research.att.com/~njas/sequences/?q=id:A129367|id:A000912&fmt=0
(a couple of terms differ at the beginning)

http://www.research.att.com/~njas/sequences/?q=id:A093668|id:A000926&fmt=0
(Same values, both conjectured to be finite)


These two sequences:

http://www.research.att.com/~njas/sequences/?q=id:A004306|id:A000803&fmt=0

are the same from "24" onwards. Will they always be the same after that
point?