IJPAM: Volume 91, No. 1 (2014)

More on the Diophantine equation $3^x + 85^y = z^2$

Banyat Sroysang
Department of Mathematics and Statistics
Faculty of Science and Technology
Thammasat University, Rangsit Center
Pathumthani, 12121, THAILAND

Abstract. In this paper, we show that $(1,0,2)$ is a unique non-negative integer solution $(x,y,z)$ for the Diophantine equation $3^x + 85^y = z^2$ where $x,y$ and $z$ are non-negative integers. This result implies that $(1,0,0,2)$ is a solution $(x,u,v,z)$ for the Diophantine equation $3^x + 5^u 17^v = z^2$.

Received: January 14, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v91i1.13 How to cite this paper?
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 91
Issue: 1