On a Connection of Number Theory with Graph Theory

DOI10.1023/B:CMAJ.0000042385.93571.58zbMath1080.11004OpenAlexW2056833032MaRDI QIDQ3366643

Michal Křížek, Lawrence Somer

Publication date: 14 February 2006

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

Full work available at URL: https://eudml.org/doc/30876

zbMATH Keywords

digraphsprimalitygroup theoryChinese remainder theoremFermat numbers

Mathematics Subject Classification ID

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

Related Items (28)

The digraphs arising by the power maps of generalized quaternion groups ⋮ The cubic mapping graph for the ring of Gaussian integers modulo n ⋮ On the heights of power digraphs modulo n ⋮ Structures of power digraphs over the congruence equation \(x^p\equiv y\; (\text{mod}\; m)\) and enumerations ⋮ The Iteration Digraphs of Lambert Map Over the Local Ring $mathbb{Z}/p^kmathbb{Z}$ : Structures and Enumerations ⋮ The Square Mapping Graphs of Finite Commutative Rings ⋮ Unnamed Item ⋮ On iteration digraph and zero-divisor graph of the ring ℤ n ⋮ The classification of finite groups by using iteration digraphs ⋮ On the symmetric digraphs from powers modulo \(n\) ⋮ The structure of power digraph connected with the congruence a¹¹ ≡ b(mod n) ⋮ Unnamed Item ⋮ The structure of isomorphic digraph from powers modulo \(p^e\) ⋮ Digraph from power mapping on noncommutative groups ⋮ Exponent of local ring extensions of Galois rings and digraphs of the $k$th power mapping ⋮ THE DIGRAPH OF THE SQUARE MAPPING ON QUOTIENT RINGS OVER THE GAUSSIAN INTEGERS ⋮ Unnamed Item ⋮ On the Structure of G(H, k) ⋮ On simple graphs arising from exponential congruences ⋮ Some digraphs arising from number theory and remarks on the zero-divisor graph of the ring \(Z_n\) ⋮ The quadratic digraph on polynomial rings over finite fields ⋮ The power digraphs associated with generalized dihedral groups ⋮ Structure of digraphs associated with quadratic congruences with composite moduli ⋮ Properties of digraphs connected with some congruence relations ⋮ Symmetry of iteration graphs ⋮ On symmetric digraphs of the congruence \(x^k \equiv y \pmod n\) ⋮ On the symmetric digraphs from the kth power mapping on finite commutative rings ⋮ The structure of digraphs associated with the congruence x k ≡ y (mod n)

Cites Work

• Combinatorial cycles of a polynomial map over a commutative field
• The graph of the square mapping on the prime fields
• A necessary and sufficient condition for the primality of Fermat numbers
• Groups, Graphs, and Fermat's Last Theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item

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