O číslech spřízněných a dokonalých. [II.]
O dělitelnosti čísel dekadických jedenácti
O jednom zovšeobecnení číselnoteoretického vzťahu a jeho použití
O multiplikatívnej pologrupe zvyškových tried (mod )
O postupnostiach prirodzených čísel s ohraničeným počtom prvočíselných deliteľov
On a compositeness test for .
On a conjecture of R. L. Graham
On a conjecture of R. L. Graham
On a problem of R.L.Graham
On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions
The paper deals with lower bounds for the remainder term in asymptotics for a certain class of arithmetic functions. Typically, these are generated by a Dirichlet series of the form ζ 2(s)ζ(2s−1)ζ M(2s)H(s), where M is an arbitrary integer and H(s) has an Euler product which converges absolutely for R s > σ0, with some fixed σ0 < 1/2.
On a system of equations with primes
Given an integer , let be pairwise coprime integers , a family of nonempty proper subsets of with “enough” elements, and a function . Does there exist at least one prime such that divides for some , but it does not divide ? We answer this question in the positive when the are prime powers and and are subjected to certain restrictions.We use the result to prove that, if and is a set of three or more primes that contains all prime divisors of any number of the form for...
On an algorithm which produces the g.c.d. of a set of n (n>2) integers in a simultaneous manner.
On an extension of Kronecker's function
On certain arithmetic functions involving the greatest common divisor
The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.
On divisibility of some power sums.
On exceptions to Szegedy's theorem
On -thin sets
On happy factorizations.
On K-Stage Euclidean algorithms for Galois extensions of Q.
On multiplicatively e-perfect numbers.