IJPAM: Volume 100, No. 4 (2015)

ON THE DIOPHANTINE EQUATION $483^x+483^{2s}n^y=z^{2t}$,
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 $483^x+483^{2s}n^y=z^{2t}$ 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: December 23, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v100i4.4 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: 4
Pages: 461 - 468


$483^x+483^{2s}n^y=z^{2t}$, WHERE $s,t,n$ ARE NON-NEGATIVE INTEGERS AND $n\equiv 5\pmod{20}$%22&as_occt=any&as_epq=&as_oq=&as_eq=&as_publication=&as_ylo=&as_yhi=&as_sdtAAP=1&as_sdtp=1" title="Click to search Google Scholar for this entry" rel="nofollow">Google Scholar; DOI (International DOI Foundation); WorldCAT.

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