On a conjecture of Issai Schur.
On a problem of Narkiewicz concerning uniform distributions of sequences of integers
On a problem of Pillai and its generalizations
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On Artin's conjecture.
On characters and polynomials
On Consecutive k'th Power Residues.
On generalized square-full numbers in an arithmetic progression
Let and . Denote by the set of all integers whose canonical prime representation has all exponents
On prime primitive roots
On the asymmetric divisor problem with congruence conditions
A certain generalized divisor function is studied which counts the number of factorizations of a natural number into integer powers with prescribed exponents under certain congruence restrictions. An -estimate is established for the remainder term in the asymptotic for its Dirichlet summatory function.
On the distribution of inverses modulo p (II)
On the distribution of k-th power non residues in the interval [1, pa], ... .
On the distribution of power residues and non-residues.
On the distribution of primitive roots mod p
On the distribution of the partial sum of Euler's totient function in residue classes
We investigate the distribution of (which counts the number of Farey fractions of order n) in residue classes. While numerical computations suggest that Φ(n) is equidistributed modulo q if q is odd, and is equidistributed modulo the odd residue classes modulo q when q is even, we prove that the set of integers n such that Φ(n) lies in these residue classes has a positive lower density when q = 3,4. We also provide a simple proof, based on the Selberg-Delange method, of a result of T. Dence and...
On the Fermat periods of natural numbers.
On the generalization of the D. H. Lehmer problem II
On the least quadratic non-residue of a prime p ... 3 (mod 4).
On the parity of k-th powers modulo p. A generalization of a problem of Lehmer
On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers