A note on the exponential Diophantine equation \((a^n-1)(b^n-1)=X^2\)

DOI10.1007/s12044-019-0520-xzbMath1422.11071arXiv1801.04717OpenAlexW2965688512WikidataQ115601817 ScholiaQ115601817MaRDI QIDQ2274783

Refik Keskin

Publication date: 1 October 2019

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.04717

zbMATH Keywords

exponential Diophantine equationPell equationLucas sequence

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (2)

On the exponential Diophantine equation \((a^n-2)(b^n-2)=x^2\) ⋮ On the Diophantine equation $(2^x-1)(p^y-1)=2z^2$

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the diophantine equation \((a^n-1)(b^n-1)= x^2\)
• The product of like-indexed terms in binary recurrences
• The Diophantine equation \((a^n-1)(b^n-1)=x^2\)
• Positive integer solutions of some Diophantine equations in terms of integer sequences
• On the diophantine equation (a^n-1)(b^n-1)=x^2
• A Remark on a Paper of Luca and Walsh
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• My Numbers, My Friends
• On the exponential Diophantine equation $(a^{n}-1)(b^{n}-1)=x^{2}$
• On the Diophantine Equation mX 2 - nY 2 = ± 1
• On the Diophantine equations \((2^n-1)(6^n-1)=x^2\) and \((a^n-1)(a^{kn}-1)=x^2\)

This page was built for publication: A note on the exponential Diophantine equation \((a^n-1)(b^n-1)=X^2\)