Solution of the Diophantine equation 783x+85y=z2 ∗

Sudhanshu Agarwal; Lalit Mohan Upadhyaya

doi:10.48165/bpas.2023.42E.1.4

Authors

Sudhanshu Agarwal Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh-273402, India.
Lalit Mohan Upadhyaya Department of Mathematics, Municipal Post Graduate College, Mussoorie, Dehradun, Uttarakhand -248179, India

DOI:

https://doi.org/10.48165/bpas.2023.42E.1.4

Keywords:

Catalan’s Conjecture, Diophantine Equation, Solution

Abstract

In this paper we consider the Diophantine equation 783x + 85y = z2, 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.

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