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2 results

  • Proof of a Conjecture of Chowla and Zassenhaus on Permutation Polynomials

  • Stephen D. Cohen
  • Journal:
    Canadian Mathematical Bulletin / Volume 33 / Issue 2 / 01 June 1990
    Published online by Cambridge University Press:
    20 November 2018, pp. 230-234
    Print publication:
    01 June 1990
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  • The following conjecture of Chowla and Zassenhaus ( 1968) is proved. If f(x) is an integral polynomial of degree ≧ 2 and p is a sufficiently large prime for which f (considered modulo p) is a permutation polynomial of the finite prime field Fp, then for no integer c with 1 ≦ c < p is f(x) + cx a permutation polynomial of Fp.

  • Dickson Polynomials Over Finite Fields and Complete Mappings

  • Gary L. Mullen, Harald Niederreiter
  • Journal:
    Canadian Mathematical Bulletin / Volume 30 / Issue 1 / 01 March 1987
    Published online by Cambridge University Press:
    20 November 2018, pp. 19-27
    Print publication:
    01 March 1987
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  • Dickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.