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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.
Keywords
elliptic curves, Fermat numbers, duplication formula
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 11B37, 11G15, 11Y11
Milestones
Received: 12 August 2017
Revised: 17 July 2018
Accepted: 22 July 2018
Published: 14 December 2018
Communicated by Bjorn Poonen