IJPAM: Volume 92, No. 1 (2014)

ON TWO DIOPHANTINE EQUATIONS
$7^x + 19^y = z^2$ and $7^x + 91^y = z^2$

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 both two Diophantine equations $7^x + 19^y = z^2$ and $7^x + 91^y = z^2$ have no non-negative integer solution where $x,y$ and $z$ are non-negative integers.

Received: January 14, 2014

AMS Subject Classification: 11D61

Key Words and Phrases: exponential Diophantine equation

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DOI: 10.12732/ijpam.v92i1.10 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: 92
Issue: 1
Pages: 113 - 116

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).