IJPAM: Volume 81, No. 4 (2012)

MORE ON THE DIOPHANTINE EQUATION
$8^x + 19^y = z^2$

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 the Diophantine equation $8^x + 19^y = z^2$ has a unique non-negative integer solution. The solution $(x,y,z)$ is $(1,0,3)$.

Received: July 17, 2012

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 4