On the Solution of Diophantine Equation (πŸ‘πŸ•)πŸπ’™+(πŸπŸπ“Ύ+𝟏)π’š=π’›πŸ

  • Sudhanshu Aggarwal Assistant Professor, Department of Mathematics, National PG College, Barhalganj, Gorakhpur, Uttar Pradesh, India.
  • Deepak Kumar Assistant Professor, Department of Mathematics, S.R.P.S. College, Jaintpur, Muzaffarpur, Bihar, India.
  • Vidya Sagar Chaubey Assistant Professor, Department of Mathematics, B.R.D.P.G. College, Deoria, Uttar Pradesh, India.

Abstract

The aim of this study is to discuss the solution of the Diophantine equation (37)2π‘₯+(12π“Š+1)𝑦=𝑧2, where π“Š,π‘₯,𝑦, and 𝑧 are non-negative integers. For this, authors have used congruence modulo method. Results of this study indicate that the Diophantine equation (37)2π‘₯+(12π“Š+1)𝑦=𝑧2, where π“Š,π‘₯,𝑦, and 𝑧 are non-negative integers, has no solution in the set of non-negative integers.

Author Biography

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

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

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Published
2024-12-23
How to Cite
AGGARWAL, Sudhanshu; KUMAR, Deepak; CHAUBEY, Vidya Sagar. On the Solution of Diophantine Equation (πŸ‘πŸ•)πŸπ’™+(πŸπŸπ“Ύ+𝟏)π’š=π’›πŸ. Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 9, n. 3&4, p. 43-47, dec. 2024. ISSN 2455-7021. Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1351>. Date accessed: 21 dec. 2024.
Citation Formats
Issue
Vol 9 No 3&4 (2024): Journal of Advanced Research in Applied Mathematics and Statistics
Section
Research Article