Distribution of values of polynomial Fermat quotients

Igor E. Shparlinski; Arne Winterhof

doi:10.1016/j.ffa.2012.10.004

Distribution of values of polynomial Fermat quotients

Igor E. Shparlinski, Arne Winterhof^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Let P be an irreducible polynomial of degree n over F_q. For AF_q[X] with gcd(A,P)=1 the polynomial Fermat quotient qP(A) is defined byqP(A)≡A^qn-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.

Original language	English
Pages (from-to)	93-104
Number of pages	12
Journal	Finite Fields and their Applications
Volume	19
Issue number	1
DOIs	https://doi.org/10.1016/j.ffa.2012.10.004
Publication status	Published - Jan 2013

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abstract = "Let P be an irreducible polynomial of degree n over Fq. For AFq[X] with gcd(A,P)=1 the polynomial Fermat quotient qP(A) is defined byqP(A)≡Aqn-1-1P(modP)anddegqP(A)",

author = "Shparlinski, {Igor E.} and Arne Winterhof",

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AB - Let P be an irreducible polynomial of degree n over Fq. For AFq[X] with gcd(A,P)=1 the polynomial Fermat quotient qP(A) is defined byqP(A)≡Aqn-1-1P(modP)anddegqP(A)

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JO - Finite Fields and their Applications

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Distribution of values of polynomial Fermat quotients

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