IJPAM: Volume 100, No. 3 (2015)

ON THE DIOPHANTINE EQUATION $323^x+323^{2s}n^y=z^{2t}$
WHERE $s,t,n$ ARE NON-NEGATIVE INTEGERS
AND $n\equiv 5\pmod{20}$

S. Chotchaisthit$^1$, S. Worawiset$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Khon Kaen University
Khon Kaen 40002, THAILAND


Abstract. Let $s,t,n$ be non negative integers such that $n\equiv 5\pmod{20}$. In this paper, we found that all non-negative integer solutions $(x,y,z)$ of the Diophantine equation $323^x+323^{2s}n^y=z^{2t}$ are in the following form:

\begin{displaymath} \text{$(x,y,z)$}= \left\{ \begin{array}{cll} \textrm{$(1+2s,... ...lution} &\text{;}& \textrm{otherwise.} \\ \end{array} \right. \end{displaymath}



Received: February 7, 2015

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v100i3.11 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: 2015
Volume: 100
Issue: 3
Pages: 435 - 442


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