Skye Binegar, Randy Dominick, Meagan Kenney, Jeremy Rouse, Alex Walsh
Published 2017-08-12Version 1
The Fermat numbers have many notable properties, including order universality, coprimality, and definition by a recurrence relation. We use arbitrary elliptic curves and rational points of infinite order 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.
An Elliptic Curve Analogue of Pillai's Lower Bound on Primitive Roots
A question of Erdös on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture
A LLT-like test for proving the primality of Fermat numbers
![QR code for arXiv:1708.03804 [math.NT]](http://oss.arxitics.com/images/favicon.svg)