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

Georgi Guninski guninski at guninski.com
Sat Oct 23 17:34:19 CEST 2010

On Sat, Oct 23, 2010 at 02:25:26PM +0200, Richard Mathar wrote:
> (I am adding n=1 and n=12 etc):

thanks for catching the bug (what i originally posted seems to be n with
at least 2 unordered solutions)

i wonder if something like this will work:

pick a set of k integers x_k. for each x_k introduce 2 new variables
y_k, z_k and 2 equations:

x_k * y_k * z_k = z
x_k + y_k - z_k = 1

the resulting system has only one free variable z.

if by any chance this method works i would be interested in the rank of
the elliptic curve (for moderate rank curves working in Q instead of Z
is also an option)

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