Algebra & Number Theory Seminar
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Texas Tech University

Algebra & Number Theory Seminar

2017-2018

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Department of Mathematics & Statistics

Math 109

Wednesdays 3:00-4:00 pm

### Randy Dominick

Texas Tech University

#### Wednesday, 18 October, 2017

#### Math 109, 3:00 pm

**Title:** Elliptic Fermat Numbers

**Abstract:** 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.