arXiv
Open Access
2019
There are infinitely many rational Diophantine sextuples with square denominators
Andrej Dujella
Matija Kazalicki
Vinko Petričević
Abstrak
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 in 2016 Dujella, Kazalicki, Mikić and Szikszai proved that there are infinitely many of them. In this paper, we prove that there exist infinitely many rational Diophantine sextuples such that the denominators of all the elements in the sextuples are perfect squares.
Topik & Kata Kunci
Penulis (3)
A
Andrej Dujella
M
Matija Kazalicki
V
Vinko Petričević
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓