Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8)

Authors

  • Hasan Sankari
  • Mustafa bojakli

Abstract

 

In this research, we study the Diophantine equations of the form  which constitute algebraically abelian variety in projective space and represent, in geometric form, family of elliptic curves over field , besides to building isomorphism between this elliptic curve and subset of ring of integrals, thus find the maximal finite extension for field  and determine the number of points that are finite torsion and torsion  to this family in which we can determine some value of  such that the rank of elliptic curve above the field  equal to one.

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Published

2019-02-27

How to Cite

1.
Sankari H, bojakli M. Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8). TUJ-BA [Internet]. 2019Feb.27 [cited 2025Apr.5];39(3). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/3743

Issue

Vol. 39 No. 3 (2017): العلوم الأساسية

Section

Articles

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