Abstract
Let P be an irreducible polynomial of degree n over Fq. For A∈Fq[X] with gcd(A,P)=1 the polynomial Fermat quotient qP(A) is defined byqP(A)≡Aqn−1−1P(modP)anddegqP(A)<n. We study several properties of polynomial Fermat quotients including the number of fixed points, the image size, and multiplicity of values in the image.
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