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