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

Vandita Patel

doi:10.1007/s11139-021-00408-9

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

Vandita Patel

Pure Mathematics

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Abstract

We describe a computationally efficient approach to resolving equations of the form C1x2+C2=yn in coprime integers, for fixed values of C1, C2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.

Original language	English
Journal	The Ramanujan Journal
DOIs	https://doi.org/10.1007/s11139-021-00408-9
Publication status	Published - 2021

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title = "A Lucas–Lehmer approach to generalised Lebesgue–Ramanujan–Nagell equations",

abstract = "We describe a computationally efficient approach to resolving equations of the form C1x2+C2=yn in coprime integers, for fixed values of C1, C2 subject to further conditions. We make use of a factorisation argument and the Primitive Divisor Theorem due to Bilu, Hanrot and Voutier.",

author = "Vandita Patel",

year = "2021",

doi = "10.1007/s11139-021-00408-9",

language = "English",

journal = "The Ramanujan Journal",

issn = "1382-4090",

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AU - Patel, Vandita

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AB - We describe a computationally efficient approach to resolving equations of the form C1x2+C2=yn in coprime integers, for fixed values of C1, C2 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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DO - 10.1007/s11139-021-00408-9

M3 - Article

SN - 1382-4090

JO - The Ramanujan Journal

JF - The Ramanujan Journal

ER -

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

Abstract

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