Distribution of values of polynomial Fermat quotients

Igor E. Shparlinski, Arne Winterhof*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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)<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 languageEnglish
Pages (from-to)93-104
Number of pages12
JournalFinite Fields and their Applications
Issue number1
Publication statusPublished - Jan 2013


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