A note on the diophantine equation x<sup>2</sup> = y<sup>2</sup> + 3z<sup>2</sup>

Authors

  • Abdullah Al Kafi Majumdar Beppu-shi Oaza Tsurumi, Renace Beppu, Japan
  • Abul Kalam Ziauddin Ahmed World University of Bangladesh, Dhanmondi, Dhaka, Bangladesh

DOI:

https://doi.org/10.3329/jbas.v44i2.51464

Keywords:

Diophantine equation, S-related and Z-related triangles, Primitive solution

Abstract

In the study of 60-degree and 120-degree triangles, one encounters the Diophantine equations of the form x2 = y2 + 3z2. This paper considers the characteristics of the solution of the Diophantine equation. More specifically, it is shown that the equation has solutions of the form x= p = 3n + 1 for some integer n (>0), where p is a prime with 7£ p £199.

Journal of Bangladesh Academy of Sciences, Vol. 44, No. 2, 201-205, 2020

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Published

2021-01-19

How to Cite

Majumdar, A. A. K., & Ahmed, A. K. Z. (2021). A note on the diophantine equation x<sup>2</sup> = y<sup>2</sup> + 3z<sup>2</sup>. Journal of Bangladesh Academy of Sciences, 44(2), 201–205. https://doi.org/10.3329/jbas.v44i2.51464

Issue

Vol. 44 No. 2 (2020)

Section

Short Communication