Some results concerning the exponential Diophantine equation \((a^n-1)(b^m-1) = x^2\)

DOI10.1007/S13226-023-00391-5MaRDI QIDQ6572382

Zahra Ameur, Tarek Garici, Rachid Boumahdi

Publication date: 15 July 2024

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Chebyshev polynomialsexponential Diophantine equationPell equationLegendre symbol

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Higher degree equations; Fermat's equation (11D41)

Cites Work

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• The product of like-indexed terms in binary recurrences
• The Diophantine equation \((a^n-1)(b^n-1)=x^2\)
• On the exponential Diophantine equation \((a^n-1)(b^n-1)=x^2\)
• On the diophantine equation \((2^n-1)(3^n-1)=x^2\)
• A note on the exponential Diophantine equation \( (a^m-1) (b^n-1)=x^2\)
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• A note on the exponential Diophantineequation(𝑎𝑛−1)(𝑏𝑛−1) =𝑥2
• On the exponential Diophantine equation $(a^{n}-1)(b^{n}-1)=x^{2}$
• On the Diophantine equations \((2^n-1)(6^n-1)=x^2\) and \((a^n-1)(a^{kn}-1)=x^2\)

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