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