More on Diophantine Sextuples
A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Mikić and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples.
In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas for rational Diophantine sextuples.
2010 Mathematics Subject Classification11D09 11G05 11Y50
The authors acknowledge support from the QuantiXLie Center of Excellence. A.D. was supported by the Croatian Science Foundation under the project no. 6422.
- 7.T. Piezas, Extending rational Diophantine triples to sextuples (2016). http://mathoverflow.net/questions/233538/extending-rational-diophantine-triples-to-sextuples Google Scholar