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An elliptic
curve analogue to the Fermat numbers
Skye Binegar, Randy Dominick, Meagan Kenney, Jeremy Rouse and Alex Walsh
Vol. 12 (2019), No. 3, 427–449
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Abstract |
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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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Keywords
elliptic curves, Fermat numbers, duplication formula
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Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 11B37, 11G15, 11Y11
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Milestones
Received: 12 August 2017
Revised: 17 July 2018
Accepted: 22 July 2018
Published: 14 December 2018
Communicated by Bjorn Poonen
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Authors |
| Skye Binegar | |
| Department of Mathematics Reed College Portland, OR United States |
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| Randy Dominick | |
| Department of Mathematics &
Statistics Texas Tech University Lubbock, TX United States |
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| Meagan Kenney | |
| Department of Mathematics Bard College Annandale-on-Hudson, NY United States |
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| Jeremy Rouse | |
| Department of Mathematics and
Statistics Wake Forest University Winston-Salem, NC United States |
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| Alex Walsh | |
| Mathematics Department Brown University Providence, RI United States |
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