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• W2903527736 abstract "We develop a general framework for finding all perfect powers in sequences derived via shifting non-degenerate quadratic Lucas–Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to answer a question of Bugeaud, Luca, Mignotte and the third author by explicitly finding all perfect powers of the shape $$F_k pm 2 $$ where $$F_k$$ is the k-th term in the Fibonacci sequence." @default.
• W2903527736 created "2018-12-11" @default.
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• W2903527736 date "2019-01-30" @default.
• W2903527736 modified "2023-09-27" @default.
• W2903527736 title "Shifted powers in Lucas–Lehmer sequences" @default.
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• W2903527736 doi "https://doi.org/10.1007/s40993-019-0153-2" @default.
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