A note on the Diophantine equation \(x^2 =4p^n -4p^m +\ell^2\)

DOI10.1007/s13226-021-00197-3zbMath1505.11057OpenAlexW3212510369MaRDI QIDQ2095064

Fadwa S. Abu Muriefah, Gökhan Soydan, Maohua Le

Publication date: 9 November 2022

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

Full work available at URL: https://doi.org/10.1007/s13226-021-00197-3

zbMATH Keywords

Baker's methodgeneralized Ramanujan-Nagell equationpolynomial-exponential Diophantine equation

Mathematics Subject Classification ID

Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Cites Work

• On the Diophantine equation \(y^2-D=2^k\)
• Two-weight ternary codes and the equation \(y^2=4 \times 3^\alpha+13\)
• The diophantine equation \(x^ 2=4q^{a/2}+4q+1\), with an application to coding theory
• The diophantine equation \(x^ 2=4q^ n-4q+1\)
• On the number of solutions of the generalized Ramanujan-Nagell equation
• Existence of primitive divisors of Lucas and Lehmer numbers
• Linear forms in two logarithms and interpolation determinants II
• On the generalized Ramanujan-Nagell equation $x^{2} - D = p^{n}$
• Squares with Three Nonzero Digits
• The Diophantine Equation x 2 = 4q n + 4q m + 1
• On the diophantine equation 𝑥²=4𝑞^{𝑚}-4𝑞ⁿ+1
• An upper bound for least solutions of the exponential Diophantine equation D₁x² - D₂y² = λk^z
• Unnamed Item

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