On the Diophantine Equation (x2 + 1) (y2 + 4) + 2(2x − y) (2 − xy) = 4 (1 + 2xy)

Authors

  • Sudhanshu Aggarwal Assistant Professor, Department of Mathematics, National PG College, Barhalganj, Gorakhpur, Uttar Pradesh, India.
  • Vidya Sagar Chaubey Department of Mathematics, B.R.D.P.G. College, Deoria, Uttar Pradesh, India
  • Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India
  • Sanjay Kumar Department of Mathematics, M.S. College, Saharanpur, Uttar Pradesh, India

Keywords:

Integers, Solution, Diophantine Equation, Divisors

Abstract

In this paper, authors examine the Diophantine equation (x2 + 1) (y2 + 4) + 2(2x − y) (2 − xy) = 4 (1 + 2xy), where x, and y are integers, for finding it’s integer solution/s. Results of this paper indicate that this equation has eight solutions in the set of integers. These are (x,y) = (1,3), (−3,1), (0,4), (−2,0), (−2,4), (0,0), (−3,3), and (1,1).

How to cite this article:
Aggarwal S, Chaubey V S, Upadhyaya LM, Kumar S, On the Polynomial Diophantine Equation(x2 + 1) (y2 + 4) + 2(2x − y) (2 − xy) = 4 (1 + 2xy) J Adv Res Appl Math Stat, Vol 10, Issue 3&4 2025: Pg. No. 45-50.

DOI: https://doi.org/10.24321/2455.7021.202514

Author Biography

Sudhanshu Aggarwal, Assistant Professor, Department of Mathematics, National PG College, Barhalganj, Gorakhpur, Uttar Pradesh, India.

https://orcid.org/0000-0001-6324-1539

Published

2025-12-29

Issue

Vol. 10 No. 3&4 (2025): Journal of Advanced Research in Applied Mathematics and Statistics

Section

Research Article