IJPAM: Volume 97, No. 2 (2014)

ON THE DIOPHANTINE EQUATION $3^x+3^{2s}n^y=z^{2t}$
WHERE $n,s,t$ ARE NON-NEGATIVE INTEGERS
AND $n\equiv 5\pmod{20}$

N. Sarasit$^1$, S. Chotchaisthit$^2$
$^1$Department of Mathematics
Faculty of Engineering Rajamangala University of Technology Isan
Khon Kaen, 40000, THAILAND
$^2$Department of Mathematics
Faculty of Science Khon Kaen University
Khon Kaen, 40002, THAILAND


Abstract. In this paper, let $n,s,t$ be any non-negative integers where $n\equiv 5\pmod{20}$. We show that all non-negative integer solution $(x,y,z)$ of the Diophantine equation $3^x+3^{2s}n^y=z^{2t}$ are the following:

\begin{displaymath} \text{$(x,y,z)$}= \left\{ \begin{array}{cll} \textrm{$(1+... ...tion} &\text{;}& \textrm{otherwise.} \\ \end{array} \right. \end{displaymath}



Received: June 30, 2014

AMS Subject Classification: 11D16

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v97i2.9 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: 97
Issue: 2
Pages: 211 - 218


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