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Silverman, J. H., A Friendly Introduction to Number Theory. 4th Ed. Upper Saddle River: Pearson, 141-157, 2013.

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Article

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

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


Turkish Journal of Analysis and Number Theory. 2019, Vol. 7 No. 2, 50-55
DOI: 10.12691/tjant-7-2-4
Copyright © 2019 Science and Education Publishing

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.

Correspondence to: Özen  ÖZER, Department of Mathematics, Faculty of Science and Arts, Kırklareli University, Kırklareli, 39100, Turkey. Email: ozenozer39@gmail.com

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.

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