Dissertation/Thesis Abstract

Value sets of polynomials modulo a prime
by Eldanaf, Diaa S., M.S., California State University, Long Beach, 2011, 56; 1499153
Abstract (Summary)

If f (x) is a polynomial with coefficients in the finite field [special characters omitted] with p elements, then as a ranges over the elements of [special characters omitted], the number Vf of distinct values of f (a) cannot be greater than p. As a lower bound, if the degree d of f is at least 1, then it is easy to establish that Vf ≥ [special characters omitted] + 1, where [ ] denotes the greatest integer function.

In this thesis further results about Vf will be given. In particular, exact formulas for Vf will be given for quadratics, cubics and certain quartic polynomials. All polynomials with 1 ≤ d < p and Vf ≥ [special characters omitted] + 1 will be determined.

Indexing (document details)
Advisor: Valentini, Robert
School: California State University, Long Beach
School Location: United States -- California
Source: MAI 50/01M, Masters Abstracts International
Subjects: Mathematics
Publication Number: 1499153
ISBN: 978-1-124-85207-2
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