The structure of digraphs associated with the congruence x k ≡ y (mod n)

DOI10.1007/s10587-011-0079-xzbMath1249.11006OpenAlexW2469032810MaRDI QIDQ3118023

Lawrence Somer, Michal Křížek

Publication date: 1 March 2012

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/196799

zbMATH Keywords

digraphprimitive rootcongruenceChinese Remainder TheoremFermat primeSophie Germain prime

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Directed graphs (digraphs), tournaments (05C20) Factorization; primality (11A51)

Related Items (7)

On the tree structure of the power digraphs modulo n ⋮ The fundamental constituents of iteration digraphs of finite commutative rings ⋮ On iteration digraph and zero-divisor graph of the ring ℤ n ⋮ Functional graphs of families of quadratic polynomials ⋮ Functional graphs of polynomials over finite fields ⋮ The structure of power digraph connected with the congruence a¹¹ ≡ b(mod n) ⋮ Linear dynamical systems of dimension two over the ring of integers modulo pt

Cites Work

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• On symmetric digraphs of the congruence \(x^k \equiv y \pmod n\)
• On the iteration of certain quadratic maps over GF(\(p\)).
• On the cycle structure of repeated exponentiation modulo a prime
• Structure of digraphs associated with quadratic congruences with composite moduli
• Period of the power generator and small values of Carmichael’s function
• On a Connection of Number Theory with Graph Theory
• Symmetry of iteration graphs
• The iterated Carmichael λ-function and the number of cycles of the power generator
• On the periods of the linear congruential and power generators

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