• Publications
  • Influence
On a Connection of Number Theory with Graph Theory
We assign to each positive integer n a digraph whose set of vertices is H = {0, 1, ..., n − 1} and for which there is a directed edge from a ∈ H to b ∈ H if a2 ≡ b (mod n). We establish necessary andExpand
  • 41
  • 4
  • PDF
On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers
We examine densities of several sets connected with the Fermat numbers Fm=22m+1. In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We alsoExpand
  • 20
  • 4
17 lectures on Fermat numbers : from number theory to geometry
Foreword by Alena Solcova.- Table of Contents.- Preface.- Glossary of Symbols.- Introduction.- Fundamentals of Number Theory.- Basic Properties of Fermat Numbers.- The Most Beautiful Theorems onExpand
  • 61
  • 3
  • PDF
On symmetric digraphs of the congruence xk = y (mod n)
TLDR
We assign to each pair of positive integers n and k>=2 a digraph G(n,k) whose set of vertices is H={0,1,...,n-1} and for which there is a directed edge from a@? H to b@?H if a^k=b(modn). Expand
  • 28
  • 2
Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences
Shah [4] and Bruckner [1] showed that if p is a prime and p > 7, then the Fibonacci sequence {Fn} has an incomplete system of residues modulo p. Shah established this result for the cases in which pExpand
  • 12
  • 2
Structure of digraphs associated with quadratic congruences with composite moduli
We assign to each positive integer n a digraph G(n) whose set of vertices is H={0,1,...,n-1} and for which there exists a directed edge from a@?H to b@?H if a^2=b(modn). Associated with G(n) are twoExpand
  • 26
  • 1
  • PDF
Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts
Let (U) = U(P y ,Q) be a Lucas sequence of the first kind (LSFK) and let (V) = V(P,Q) be a Lucas sequence of the second kind (LSSK) each satisfying the same second-order recursion relation $$Expand
  • 12
  • 1
On the symmetric digraphs from the kth power mapping on finite commutative rings
  • Guixin Deng, L. Somer
  • Mathematics, Computer Science
  • Discret. Math. Algorithms Appl.
  • 2 February 2015
TLDR
For a finite commutative ring R and a positive integer k, let G(R, k) denote the digraph whose set of vertices is R and for which there is a directed edge from a to ak. Expand
  • 2
  • 1
A CRITIQUE OF THE STANDARD COSMOLOGICAL MODEL
According to the standard cosmological model, 27 % of the Universe consists of some mysterious dark matter, 68 % consists of even more mysterious dark energy, whereas only less than 5 % correspondsExpand
  • 4
  • 1
  • PDF
...
1
2
3
4
5
...