eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2019-04-13 7 2 50 55 10.12691/tjant-7-2-4 TJANT2019724 article Özen ÖZER ozenozer39@gmail.com 1 Department of Mathematics, Faculty of Science and Arts, K?rklareli University, K?rklareli, 39100, Turkey 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. http://pubs.sciepub.com/tjant/7/2/4/tjant-7-2-4.pdf non-extendable D(s) diophantine triples pell equations integral solutions quadratic reciprocity theorem modular arithmetic legendre/jacobi symbol