The Euler φ-Function in the Gaussian Integers

DOI10.2307/2322785zbMath0525.12001OpenAlexW4248263889MaRDI QIDQ3039440

James T. Cross

Publication date: 1983

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2322785

zbMATH Keywords

primitive rootsGaussian integersChinese remainder theoremstructure of residue class ring

Mathematics Subject Classification ID

Quadratic extensions (11R11) Congruences; primitive roots; residue systems (11A07) Arithmetic functions; related numbers; inversion formulas (11A25) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (20)

The cubic mapping graph for the ring of Gaussian integers modulo n ⋮ Structure of cubic mapping graphs for the ring of Gaussian integers modulo n ⋮ Unit group structure of the quotient ring of a quadratic ring ⋮ Unnamed Item ⋮ The Complement Graph for Gaussian Integers Modulon ⋮ RSA cryptosystem for Dedekind rings ⋮ Unit groups of quotient rings of complex quadratic rings ⋮ Fermat test with Gaussian base and Gaussian pseudoprimes ⋮ THE EULER TOTIENT FUNCTION ON QUADRATIC FIELDS ⋮ On graphs associated to ring of Guassian integers and ring of integers modulo \(n\) ⋮ Distribution of values of general Euler totient function ⋮ Zero Divisor Graph for the Ring of Gaussian Integers Modulon ⋮ Group structure computations in finite chain rings ⋮ THE DIGRAPH OF THE SQUARE MAPPING ON QUOTIENT RINGS OVER THE GAUSSIAN INTEGERS ⋮ A survey on the Intersection graphs of ideals of rings ⋮ Fuchs' problem for \(p\)-groups ⋮ An Euler phi function for the Eisenstein integers and some applications ⋮ Units on the Gauss extension of a Galois ring ⋮ The Golomb topology on a Dedekind domain and the group of units of its quotients ⋮ Unnamed Item

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