IJPAM: Volume 81, No. 4 (2012)

ON THE DIOPHANTINE EQUATION
$31^x + 32^y = z^2$

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 $31^x + 32^y = z^2$ has no non-negative integer solution.

Received: July 17, 2012

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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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