On the value set of Fermat quotients

DOI10.1090/S0002-9939-2011-11203-6zbMath1305.11003OpenAlexW2021021392MaRDI QIDQ5389381

Igor E. Shparlinski

Publication date: 26 April 2012

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2011-11203-6

zbMATH Keywords

value setFermat quotientspreimage

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Congruences; primitive roots; residue systems (11A07)

Related Items (15)

ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS ⋮ Trace representation and linear complexity of binary sequences derived from Fermat quotients ⋮ On \(k\)-error linear complexity of pseudorandom binary sequences derived from Euler quotients ⋮ On the k-error linear complexity of binary sequences derived from polynomial quotients ⋮ An extension of binary threshold sequences from Fermat quotients ⋮ On the additive energy of the Heilbronn subgroup ⋮ Trace representation of pseudorandom binary sequences derived from Euler quotients ⋮ On exponential sums over multiplicative subgroups of medium size ⋮ Linear complexity of binary sequences derived from Euler quotients with prime-power modulus ⋮ Linear complexity of pseudorandom sequences generated by Fermat quotients and their generalizations ⋮ Ratios of Small Integers in Multiplicative Subgroups of Residue Rings ⋮ Polynomial quotients: Interpolation, value sets and Waring's problem ⋮ Linear Complexity of Binary Threshold Sequences Derived from Generalized Polynomial Quotient with Prime-Power Modulus ⋮ Additive character sums of polynomial quotients ⋮ Statistical distribution of Fermat quotients

Cites Work

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• Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm
• Structure of Pseudorandom Numbers Derived from Fermat Quotients
• On the smallest pseudopower
• ON THE KUMMER–MIRIMANOFF CONGRUENCES
• On the 𝑝-divisibility of Fermat quotients
• New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum
• On the Euler-Kronecker constants of global fields and primes with small norms

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