Abstract
Let Fp denote the finite field of prime order p. We introduce a new natural family of polynomials in Fp[X]. These polynomials first arose from considering faithful representations of the elementary abelian group of order p2 in characteristic p. The polynomials exhibit a number of interesting special properties. For example they satisfy a three term recursion, are closely related to zigzag zero-one sequences and form strong divisibility sequences. These polynomials are shown to be closely connected to the order of appearance of prime numbers in the Fibonacci sequence, Artin's Primitive Root Conjecture, and the factorization of trinomials over finite fields.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
