Authors: Philip Gibbs
A Diophantine m-tuple is a set of m distinct non-zero integers such that the product of any two elements of the set is one less than a square. The definition can be generalised to any commutative ring. A computational search is undertaken to find Diophantine 5-tuples (quintuples) over the ring of quadratic integers Z[√D] for small positive and negative D. Examples are found for all positive square-free D up to 22, but none are found for the complex rings including the Gaussian integers.
Comments: 11 Pages.
[v1] 2018-02-14 10:10:56
Unique-IP document downloads: 59 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.