[seqfan] Re: n = x*y*z , x + y - z = 1

[Georgi Guninski]

On Mon, Oct 25, 2010 at 09:25:57PM +0300, Georgi Guninski wrote:
> On Sat, Oct 23, 2010 at 01:56:18PM +0300, Georgi Guninski wrote:
> > n = x*y*z 
> > x + y - z = 1
> > all positive integers
> > 
> > can one maximize the number of solutions ?
> >
> 
> Can the number of solutions be arbitrary large?
>

Noam Elkies shed some light on this.

xy(x+y)=n [ A088915 ] can have arbitrary large number of integral solutions via rational points on an elliptic curve + multiplication by cube.

the number of solution of xy(x+y-1)=n [ A171920 ] is unclear and Elkies construction doesn't work.