ON THE DIOPHANTINE EQUATION 𝟖𝓲+𝟕𝟏𝓳=𝓴𝟐

Authors

  • Sudhanshu Aggarwal Assistant Professor, Department of Mathematics, National PG College, Barhalganj, Gorakhpur, Uttar Pradesh, India.
  • Lalit Mohan Upadhyaya Associate Professor, Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand, India
  • Shahida A. T. Assistant Professor, Department of Mathematics, MES Mampad College, Mampad, Kerala, India.

Keywords:

Catalan Conjecture, Diophantine Equation, Integers, Solution

Abstract

In this study, authors looked for non-negative integer solutions to the Diophantine equation 8ð’¾+71ð’¿=ð“€2, where ð’¾,ð’¿,ð“€ are non-negative integers. For this, authors turned to Catalan's conjecture. The current paper's results demonstrate that there is only one non-negative integer solution to the Diophantine equation 8ð’¾+71ð’¿=ð“€2, where ð’¾,ð’¿,ð“€ are non-negative integers. This solution is provided by (ð’¾,ð’¿,ð“€ )=(1,0,3).
AMS SUBJECT CLASSIFICATION: 11D61

Author Biography

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

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

References

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Published

2024-02-03

Issue

Vol. 9 No. 1&2 (2024): Journal of Advanced Research in Applied Mathematics and Statistics

Section

Research Article