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july 2020 On the Exponential Diophantine Equation $(a^n-1)(b^n-1)=x^2$
Armand Noubissie, Alain Togbé, Zhongfeng Zhang
Bull. Belg. Math. Soc. Simon Stevin 27(2): 161-166 (july 2020). DOI: 10.36045/bbms/1594346413

Abstract

Let $a$ and $b$ be two distinct fixed positive integers such that $\min \{a,b\}> 1.$ First, we correct an oversight from [12]. Then, we show that the equation in the title with $b \equiv 3 \pmod 8$, $b$ prime and $a$ even has no solution in positive integers $n, x$. This generalizes a result of Szalay [10].

Citation

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Armand Noubissie. Alain Togbé. Zhongfeng Zhang. "On the Exponential Diophantine Equation $(a^n-1)(b^n-1)=x^2$." Bull. Belg. Math. Soc. Simon Stevin 27 (2) 161 - 166, july 2020. https://doi.org/10.36045/bbms/1594346413

Information

Published: july 2020
First available in Project Euclid: 10 July 2020

zbMATH: 07242764
MathSciNet: MR4121369
Digital Object Identifier: 10.36045/bbms/1594346413

Subjects:
Primary: 11D41, 11D61

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 2 • july 2020
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