Open AccessA note on the diophantine equation x<sup>2</sup> = y<sup>2</sup> + 3z<sup>2</sup>
Author(s) -
A. A. K. Majumdar,
Abul Kalam Ziauddin Ahmed
Publication year - 2021
Publication title -
journal of bangladesh academy of sciences
Language(s) - English
Resource type - Journals
eISSN - 2224-7270
pISSN - 0378-8121
DOI - 10.3329/jbas.v44i2.51464
Subject(s) - diophantine equation , integer (computer science) , degree (music) , prime (order theory) , physics , mathematics , combinatorics , computer science , acoustics , programming language
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