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.
Citation
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
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