IJPAM: Volume 105, No. 4 (2015)

ON THE DIOPHANTINE EQUATION $p^a+(p+1)^b=z^2$

Pavel Trojovský
Department of Mathematics
Faculty of Science
University of Hradec Králové
Rokitanského 62
50003 Hradec Králové, CZECH REPUBLIC


Abstract. In this paper, we shall prove some results related to the equation $p^a+(p+1)^b=z^2$. In particular, we shall prove that there is no solution when $p>3$, $b\geq 2$ and $z$ even.

Received: September 11, 2015

AMS Subject Classification: 11D61, 11D72

Key Words and Phrases: Diophantine equation, congruence, exponential equation

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DOI: 10.12732/ijpam.v105i4.14 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: 105
Issue: 4
Pages: 745 -


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