On the 𝑝-divisibility of Fermat quotients

DOI10.1090/S0025-5718-97-00843-0zbMath0903.11002MaRDI QIDQ4340875

Tauno Metsänkylä, Reijo Ernvall

Publication date: 15 June 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

tablesprimescyclotomic fieldspower residuesFermat's equationCatalan's equationFermat quotient matrixreduced Fermat quotient

Mathematics Subject Classification ID

Higher degree equations; Fermat's equation (11D41) Software, source code, etc. for problems pertaining to number theory (11-04) Cyclotomic extensions (11R18) Power residues, reciprocity (11A15) Primes (11A41) Values of arithmetic functions; tables (11Y70)

Related Items (28)

ON THE DISTRIBUTION OF PSEUDORANDOM NUMBERS AND VECTORS DERIVED FROM EULER–FERMAT QUOTIENTS ⋮ A class number free criterion for Catalan's conjecture. ⋮ Trace representation and linear complexity of binary sequences derived from Fermat quotients ⋮ Un nouveau critère pour l'équation de Catalan ⋮ On the k-error linear complexity of binary sequences derived from polynomial quotients ⋮ A search for primes 𝑝 such that the Euler number 𝐸_{𝑝-3} is divisible by 𝑝 ⋮ An extension of binary threshold sequences from Fermat quotients ⋮ Congruences involving the Fermat quotient ⋮ Trace representation of pseudorandom binary sequences derived from Euler quotients ⋮ On Wieferich and non-Wieferich primes with prime bases ⋮ On the linear complexity of binary threshold sequences derived from Fermat quotients ⋮ 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 ⋮ On the divisibility of Fermat quotients ⋮ Multiplicative character sums of Fermat quotients and pseudorandom sequences ⋮ On the value set of Fermat quotients ⋮ Boolean functions derived from Fermat quotients ⋮ BOUNDS OF MULTIPLICATIVE CHARACTER SUMS WITH FERMAT QUOTIENTS OF PRIMES ⋮ Probabilistic study of Fermats quotients ⋮ Solutions of the congruence 𝑎^{𝑝-1}≡1 (mod 𝑝^{𝑟}) ⋮ Class number bounds and Catalan’s equation ⋮ Hamming correlation of higher order ⋮ Trace representation of the binary \(pq^2\)-periodic sequences derived from Euler quotients ⋮ Wieferich pairs and Barker sequences ⋮ 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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• Miller's primality test
• On the generalized Wieferich criteria
• On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson
• Irregular Primes and Cyclotomic Invariants to Four Million
• New Solutions of a p - 1 ≡1 (mod p 2 )
• Catalan's Equation x p - y q = 1 and Related Congruences
• Fermat's Last Theorem (Case 1) and the Wieferich Criterion
• Refining the conditions on the Fermat quotient
• ON THE KUMMER–MIRIMANOFF CONGRUENCES
• On the nonvanishing of Fermat quotients (mod p).
• On the p-Divisibility of the Fermat Quotients
• A note on Catalan's equation
• Norm residue symbol and cyclotomic units
• Catalan's Equation Has No New Solution with Either Exponent Less Than 10651
• Cyclotomic Invariants for Primes Between 125000 and 150000
• A search for Wieferich and Wilson primes
• Note on the Congruence a p-1 ≡1 (mod p 2 )

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