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.
|School:||California State University, Long Beach|
|School Location:||United States -- California|
|Source:||MAI 50/01M, Masters Abstracts International|
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