On the Diophantine equation \(2^s + p^k = m^2\) with a Fermat prime \(p\)

DOI10.1016/J.JNT.2024.09.006MaRDI QIDQ6651551

Florian Luca, István Pink

Publication date: 10 December 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

continued fractionslinear form in logarithms\(p\)-adic approximation lattices

Mathematics Subject Classification ID

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

Cites Work

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• The diophantine equation \(x^2+7=2^n\)
• Factoring polynomials with rational coefficients
• Effective lower bound for the \(p\)-adic distance between powers of algebraic numbers
• Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson.
• The equations \(2^N\pm 2^M\pm 2^L=z^2\)
• Linear forms in two logarithms and interpolation determinants
• On the generalized Ramanujan-Nagell equation I
• Primary cyclotomic units and a proof of Catalans conjecture
• Über eine Diophantische Gleichung von Ramanujan-Nagell und ihre Verallgemeinerung

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