The Primitive-Solutions of Diophantine Equation x^2+pqy^2=z^2, for primes p,q
DOI:
https://doi.org/10.20956/j.v18i2.19018Keywords:
composite number, diophantine equation, prime number, primitive solutionAbstract
In this paper, we determine the primitive solutions of diophantine equations x^2+pqy^2=z^2, for positive integers x, y, z, and primes p,q. This work is based on the development of the previous results, namely using the solutions of the Diophantine equation x^2+y^2=z^2, and looking at characteristics of the solutions of the Diophantine equation x^2+3y^2=z^2 and x^2+9y^2=z^2.Downloads
References
Abdelalim and Dyani, 2014. The Solution of Diophantine Equation x^2+3y^2=z^2. International Journal of Algebra, Vol. 8, No. 15, pp. 729-723.
Alan M. and Zengin U. 2020. On the Diophantine equation x^2+3^a 〖41〗^b=y^n. Periodica Mathematica Hungarica, Vol. 81, No. 2, pp. 284–291.
Andreescu T., Andrica D. & Cucurezeanu I., 2010. An Introduction to Diophantine Equations: A Problem-Based Approach, Birkhäuser (Springer Science+Business Media LLC), Boston.
Burshtein, N. 2020. Solutions of the Diophantine Equation p^x + p^y = z^4 when p≥2 are is Primes and x,y,z are Positive Integers. Annals of Pure and Applied Mathematics, Vol. 21, No. 2, pp. 125-128.
Chakraborty K. and Hoque A. 2021. On the Diophantine Equation dx^2+p^2a q^2b=4y^p. Results in Mathematics, Vol. 77, pp. 18.
Rahman, S.I. & Hidayat, N., 2018. Solusi Primitif Persamaan Diophantine x^2+9y^2=z^2. Prosiding Konferensi Nasional Matematika (KNM), XIX, pp. 71-76, Himpunan Matematika Indonesia (IndoMS) Perwakilan Surabaya, Surabaya.
Rahmawati R., Sugandha A., Tripena A. and Prabowo A. 2018. The Solution for the Non-linear Diophantine Equation (7k -1)^x +(7k)^y = z^2 with k as the positive even whole number. Journal of Physics: Conference Series, Vol. 1179, The 1st International Conference on Computer, Science, Engineering and Technology 27–28 November 2018, Tasikmalaya, Indonesia.
Rosen, K.H. 1984. Elementary Number Theory and Its Applications, Perason, Boston.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Author and publisher
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Matematika, Statistika dan Komputasi is an Open Access journal, all articles are distributed under the terms of the Creative Commons Attribution License, allowing third parties to copy and redistribute the material in any medium or format, transform, and build upon the material, provided the original work is properly cited and states its license. This license allows authors and readers to use all articles, data sets, graphics and appendices in data mining applications, search engines, web sites, blogs and other platforms by providing appropriate reference.
