On the Polynomial Diophantine Equation (x2 - 10x + y2 - 4y + 24) = 0

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
  • Dinesh Thakur Department of Mathematics, Bahra University, Waknaghat District Solan, Himachal Pradesh, India
  • Arvind Salve Department of Mathematics, Dr. S.D.D. Arts College and Commerce and Science College, Wada, Maharashtra, India

Keywords:

Integers, Solution, Polynomial Diophantine Equation, Continued Fraction

Abstract

In this paper, authors examine the polynomial Diophantine equation (x2 - 10x + y2 - 4y + 24) = 0, 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) = (7,3), (6,4), (3,3), (6,0), (4,4), (7,1), (3,1), and (4,0).

DOI: https://doi.org/10.24321/2455.7021.202604

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

2026-05-15

Issue

Vol. 11 No. 1&2 (2026): Journal of Advanced Research in Applied Mathematics and Statistics

Section

Research Article