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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 and… Expand

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 also… Expand

20 4

17 lectures on Fermat numbers : from number theory to geometry

- M. Krízek, F. Luca, L. Somer, A. Solcova
- Mathematics
- 2001

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 on… Expand

61 3- PDF

On symmetric digraphs of the congruence xk = y (mod n)

TLDR

28 2

Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences

- L. Somer
- Mathematics
- 1988

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 p… Expand

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 two… Expand

26 1- PDF

Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts

- L. Somer
- Mathematics
- 1996

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

Bounds for frequencies of residues of regular second-order recurrences modulo pr

- Walter Carlip, L. Somer
- Mathematics
- 31 January 1999

9 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

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2 1

A CRITIQUE OF THE STANDARD COSMOLOGICAL MODEL

- L. Somer
- Physics
- 2014

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 % corresponds… Expand

4 1- PDF

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