O devátém Hilbertově problému
On A Conjecture of Emma Lehmer.
On a conjecture of Issai Schur.
On a conjecture of Norton
On a connection of number theory with graph theory
We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.
On Alternatives of Polynomial Congruences
What should be assumed about the integral polynomials in order that the solvability of the congruence for sufficiently large primes p implies the solvability of the equation in integers x? We provide some explicit characterizations for the cases when are binomials or have cyclic splitting fields.
On anti-elite prime numbers.
On character sums and the non-vanishing for s > 0 of Dirichlet L-series belonging to real odd characters χ
On Consecutive k'th Power Residues.
On explicit reciprocity laws.
On explicit reciprocity laws. II.
On generalized elite primes.
On Lucas pseudoprimes of the form in arithmetic progression with a prescribed value of the Jacobi symbol
On power residues
On power residues
On primitive roots.
On pseudoprime numbers of special form
On semiregular digraphs of the congruence
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . The digraph is semiregular if there exists a positive integer such that each vertex of the digraph has indegree or 0. Generalizing earlier results of the authors for the case in which , we characterize all semiregular digraphs when is arbitrary.
On some special quartic reciprocity laws
On strong Lehmer pseudoprimes in the case of negative discriminant in arithmetic progressions