IJPAM: Volume 90, No. 1 (2014)

ON THE DIOPHANTINE EQUATION $8^x + 13^y = z^2$

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


Abstract. In this paper, we prove that the Diophantine equation $8^x + 13^y = z^2$ has a unique non-negative integer solution where $x$, $y$ and $z$ are non-negative integers. The solution $(x,y,z)$ is $(1,0,3)$.

Received: September 27, 2013

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v90i1.9 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 1