On the solutions of the equation x² + 19^m = yⁿ

Bilge Peker and Selin (İnağ) Çenberci
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 2, Pages 34–41
Full paper (PDF, 208 Kb)

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Authors and affiliations

Bilge Peker
Elementary Mathematics Education, Ahmet Kelesoglu Education Faculty Konya Necmettin Erbakan University

Selin (İnağ) Çenberci
Department of Mathematics, Ahmet Kelesoglu Education Faculty Konya Necmettin Erbakan University

Abstract

In this article, we consider the equation x² + 19^m = yⁿ, m > 0. We find the solutions of the title equation for not only 2 ∣ m but also 2 ∤ m.

Keywords

• Exponential Diophantine equation
• Primitive divisors
• Quadratic field

AMS Classification

• 11D41
• 11D61

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