On the Diophantine equations z<sup>2</sup> = k(k<sup>2</sup> + 3) and z<sup>2</sup> = k(k<sup>2</sup> + 12)

Authors

  • Shah Mohammad Shahidul Islam Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh
  • Abdullah Al Kafi Majumdar 1Ritsumeikan Asia-Pacific University, Beppu-shi 874–8577, Japan

DOI:

https://doi.org/10.3329/jbas.v45i1.54265

Keywords:

Diophantine equation, analytic solution, GP/PARI

Abstract

This paper provides an analytical method of finding all the (positive, integral) solutions of the Diophantine equation z2 = k(k2+3). We also prove analytically that the Diophantine equation z2 = k(k2+12) has no positive, integer solution.

J. Bangladesh Acad. Sci. 45(1); 127-129: June 2021

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Published

2021-07-15

How to Cite

Islam, S. M. S., & Kafi Majumdar, A. A. (2021). On the Diophantine equations z<sup>2</sup> = k(k<sup>2</sup> + 3) and z<sup>2</sup> = k(k<sup>2</sup> + 12). Journal of Bangladesh Academy of Sciences, 45(1), 127–129. https://doi.org/10.3329/jbas.v45i1.54265

Issue

Vol. 45 No. 1 (2021)

Section

Short Communication