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An elliptic curve analogue to the Fermat numbers. (English) Zbl 1442.11091
Summary: 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.
MSC:
11G05 Elliptic curves over global fields
11B37 Recurrences
11G15 Complex multiplication and moduli of abelian varieties
11Y11 Primality
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