On the Quadratic Diophantine Equation (x1x2 ) + x1 x2 = 8

  • Sudhanshu Aggarwal Assistant Professor, Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar-Pradesh, India
  • Lalit Mohan Upadhyaya Associate Professor, Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India
  • Swarg Deep Sharma Assistant Professor, Nand Lal Singh College, Jaitpur-Daudpur, Saran, Bihar, Constituent College of J.P. University, Chhapra, Saran, Bihar, India

Abstract

In this paper, authors have studied the quadratic Diophantine equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8; ð‘¥1,ð‘¥2 ∈ ð‘−{0}, where ð‘−{0} represents the set of non zero integers, for determining the ordered pairs (ð‘¥1,ð‘¥2) ∈ ð‘−{0} × ð‘−{0} that satisfy the equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8. It was shown by the results that the ordered pairs (ð‘¥1,ð‘¥2) = (4,1),(−4,−1) ∈ ð‘−{0} × ð‘−{0} are the only solutions of the quadratic Diophantine equation (ð‘¥1 ð‘¥2 ) +ð‘¥1ð‘¥2 = 8.

Author Biography

Sudhanshu Aggarwal, Assistant Professor, Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar-Pradesh, India

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

Published
2025-08-14
How to Cite
AGGARWAL, Sudhanshu; UPADHYAYA, Lalit Mohan; SHARMA, Swarg Deep. On the Quadratic Diophantine Equation (x1x2 ) + x1 x2 = 8. Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 10, p. 16-19, aug. 2025. ISSN 2455-7021. Available at: <https://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1617>. Date accessed: 27 dec. 2025.
Citation Formats
Issue
Vol 10 (2025): (Special Issue): Journal of Advanced Research in Applied Mathematics and Statistics
Section
Research Article