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2019 An elliptic curve analogue to the Fermat numbers
Skye Binegar, Randy Dominick, Meagan Kenney, Jeremy Rouse, Alex Walsh
Involve 12(3): 427-449 (2019). DOI: 10.2140/involve.2019.12.427

Abstract

The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use rational points of infinite order on elliptic curves to generate sequences that are analogous to the Fermat numbers. We demonstrate that these sequences have many of the same properties as the Fermat numbers, and we discuss results about the prime factors of sequences generated by specific curves and points.

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Skye Binegar. Randy Dominick. Meagan Kenney. Jeremy Rouse. Alex Walsh. "An elliptic curve analogue to the Fermat numbers." Involve 12 (3) 427 - 449, 2019. https://doi.org/10.2140/involve.2019.12.427

Information

Received: 12 August 2017; Revised: 17 July 2018; Accepted: 22 July 2018; Published: 2019
First available in Project Euclid: 5 February 2019

zbMATH: 07033140
MathSciNet: MR3905339
Digital Object Identifier: 10.2140/involve.2019.12.427

Subjects:
Primary: 11G05
Secondary: 11B37, 11G15, 11Y11

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 3 • 2019
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