A Certain Type of Regular Diophantine Triples and Their Non-Extendability

Özen ÖZER^1,

¹Department of Mathematics, Faculty of Science and Arts, Kırklareli University, Kırklareli, 39100, Turkey

Cite this paper:
Özen ÖZER. A Certain Type of Regular Diophantine Triples and Their Non-Extendability. Turkish Journal of Analysis and Number Theory. 2019; 7(2):50-55. doi: 10.12691/tjant-7-2-4

Abstract

In the present paper, we consider some D(s) Diophantine triples for a prime integer s with its negative case/value although there exist infinitely many Diophantine triples. We give several properties of such Diophantine triples and prove that they are non – extendability to D(s) Diophantine quadruple using algebraic and elementary number theory structures.

Keywords:
non-extendable D(s) diophantine triples pell equations integral solutions quadratic reciprocity theorem modular arithmetic legendre/jacobi symbol

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