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Research articles

ScienceAsia 37 (2011): 152-159 |doi: 10.2306/scienceasia1513-1874.2011.37.152

Some families of Diophantine quadruples

Supawadee Prugsapitaka,*, Vichian Laohakosolb

ABSTRACT:     A Diophantine quadruple is a set of four positive integers such that the product of any two increased by one is a perfect square of an integer. Here we find general families of the Diophantine quadruple problem using solutions of a second order recurrence relation over a ring of integers in a number field and a polynomial ring over a field of characteristic zero.

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a Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University
b Department of Mathematics, Faculty of Science, Kasetsart University and Centre of Excellence in Mathematics, CHE, Si Ayutthya Road, Bangkok 10400, Thailand

* Corresponding author, E-mail: supawadee.p@psu.ac.th

Received 23 Dec 2010, Accepted 4 Apr 2011