A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations

We describe a computationally efficient approach to resolving equations of the form C 1 x 2 + C 2 = y n in coprime integers, for fixed values of C 1 , C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.

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Bibliographic Details
Published inThe Ramanujan journal Vol. 56; no. 2; pp. 585 - 596
Main Author Patel, Vandita
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2021
Springer Nature B.V
Subjects
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Lehmer sequences
11D59
Secondary 11D41
Primitive divisor theorem
Thue equation
Primary 11D61
Exponential equation
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Summary:We describe a computationally efficient approach to resolving equations of the form C 1 x 2 + C 2 = y n in coprime integers, for fixed values of C 1 , C 2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-021-00408-9