Primes representing by binary quadratic form

Authors

  • Hassan sankri
  • Abdullah hinnawi

Abstract

 

We  study  in  this  paper   representing   prime  integers  by  binary   quadratic   form       for  this case     (q  is  prime)  and   class  number    Depending  on the  definitions and theorems   about  binary  quadratic  form particularly on genus definition beside  the  solvability of equation    and  then we  applied  our  study  on  forms     and

 

References

MOLLIN,A.R.advanced number theory with applictions,CRC,Canada,2010,481.

BUELL,D.A. Binary quadratic forms classical and modern computations ,springer, newhom,1989.

HARVEY,C. Advanced number theory ,inc .newhom.1962.275.

] MOLLIN,A.R. algebraic number theory.2nd,CRC ,Canada,2011.417.

BUCHAMAN,J;VOLLMER,U. binary quadratic forms an algorithmic approach,springer,2007,326.

KENNETH,H.R. elementary number theory and it's applications ,Massachusetts Menlo park,California,1984.462.

FRANZ,H.K. quadratic irrationals an introduction to classical number theory,ucm,Madrid.2013.

ANTHONY,W.K. advanced algebra, east Setauket, new hom.2016.758.

ERNST,k.quadratic forms and elliptic curves, queen's university,2012.100.

سنكري.حسن.دراسة قابلية حل المعادلة الديوفانتية في مجموعة الأعداد الصحيحة الموجبة.مجلة جامعة تشرين .المجلد33.العدد11. 2011. 50-63.

CHRISTPPHER.K.thomas.On representations of integers by the quadratic form x^2-Dy^2, Rochester Institute of Technology, 2012.

JOSH,K.Binary quadratic forms, genus theory and primes of the forms p=x^2+ny^2 ,University of Chicago,2014.

IRVING,K.The forms x^2+32y^2 and x^2+64y^2,American mathematical society,2003.

CHRISTPPHER, Numbers Represented by a Finite Set of Binary Quadratic Forms,2017.

DAVID,B.Five peculiar theorems on simultaneous representation of primes by quadratic forms, Institute for mathematic fag, Københavns University.2009.

NIHAL,B.Representation of Prime Powers by Binary Quadratic Forms. C¸ankırı Karate in University,2012.

ZAMAN,A.Primes represented by positive definite binary quadratic forms,Cornell university,2017.

NOORDSIJ,j. Primes of the form x2 + ny2, Leiden University,2015.

http://www.numbertheory.org

http://www.numbertheory.org/php/classnopos.html

Downloads

Published

2018-12-23

How to Cite

1.
sankri H, hinnawi A. Primes representing by binary quadratic form. TUJ-BA [Internet]. 2018Dec.23 [cited 2024Nov.24];40(6). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/5712

Issue

Vol. 40 No. 6 (2018): العلوم الاساسية

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series  

 Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series .  The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series   Publisher

 

journal uses a CC BY-NC-SA license which mean

You are free to:

  • Adapt — remix, transform, and build upon the material
  •  
  • The licensor cannot revoke these freedoms as long as you follow the license terms.

 

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.