Pure powers in recurrence sequences and some related diophantine equations

DOI10.1016/0022-314X(87)90071-0zbMath0624.10009OpenAlexW2019586508WikidataQ106076157 ScholiaQ106076157MaRDI QIDQ1092077

Tarlok N. Shorey, Cameron L. Stewart

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0022-314x(87)90071-0

zbMATH Keywords

linear recurrence sequenceperfect powers in sequences

Mathematics Subject Classification ID

Recurrences (11B37) Higher degree equations; Fermat's equation (11D41) Linear Diophantine equations (11D04)

Related Items (17)

Powers in recurrence sequences: Pell equations ⋮ Diophantine equations with linear recurrences. An overview of some recent progress ⋮ Generalized Cullen numbers in linear recurrence sequences ⋮ Shifted powers in binary recurrence sequences ⋮ PERFECT POWERS IN PRODUCTS OF TERMS OF ELLIPTIC DIVISIBILITY SEQUENCES ⋮ Applications of the Subspace Theorem to Certain Diophantine Problems ⋮ Divisor divisibility sequences on tori ⋮ On the Diophantine equation \(p^{x_1} - p^{x_2} = q^{y_1} - q^{y_2}\) ⋮ Diophantine inequalities with power sums ⋮ Power classes of recurrence sequences ⋮ Perfect powers in products of arithmetical progressions with fixed initial term ⋮ Diophantine inequalities involving several power sums ⋮ Power values of certain quadratic polynomials ⋮ On special extrema of polynomials with applications to Diophantine problems ⋮ Diophantine equations with power sums and universal Hilbert sets ⋮ Unnamed Item ⋮ The product of like-indexed terms in binary recurrences

Cites Work

• On \(S\)-integral solutions of the equation \(y^ m=f(x)\)
• Perfect powers in second order linear recurrences
• On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.
• A sharpening of the bounds for linear forms in logarithms II
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