Solution of the Diophantine equation ${783}^x+{85}^y=z^2$∗
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Solution of the Diophantine equation ${783}^x+{85}^y=z^2$∗
Sudhanshu Agarwal1 and Lalit Mohan Upadhyaya2
BPAS-E-Math and Stat. Vol.42E(1) June 2023
DOI: 10.48165/bpas.2023.42E.1.4
Page: 31-35
Description
Description
Solution of the Diophantine equation ${783}^x+{85}^y=z^2$∗
Sudhanshu Agarwal1 and Lalit Mohan Upadhyaya2
- Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh-273402, India.
- Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand -248179, India.
- E-mail: sudhanshu30187@gmail.com
- E-mail: lmupadhyaya@rediffmail.com , hetchres@gmail.com
Communicated, edited and typeset in Latex by Jyotindra C. Prajapati (Editor).
Received October 12, 2022 / Revised April 16, 2023 / Accepted May 08, 2023. Online First Published
on June 30, 2023 at https://www.bpasjournals.com/.
Abstract
In this paper we consider the Diophantine equation ${783}^x+{85}^y=z^2$, where $x,y,z$ are non-negative integers and determine the non-negative integer solutions of this equation. Our result shows that $(x, y, z) = (1, 0, 28)$ is a unique non-negative integer solution of this equation.
Key words Catalan’s Conjecture, Diophantine Equation, Solution.
2020 Mathematics Subject Classification 11D61
