On the number of prime factors of integers of the form ab + 1
On the number of representations of integers as the sum of k terms
On the number of semigroups of natural numbers.
On the number of solutions of exponential congruences
On the number of subgroups of given index in the modular group.
On the number of subsets of relatively prime to and asymptotic estimates.
On the number of subsets relatively prime to an integer.
On the number of sums and products
On the number of ways of writing as a product of factorials.
On the Olson and the Strong Davenport constants
A subset of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, -groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general...
On the order of lacunary sums of binomial coefficients.
On the parity of the number of multiplicative partitions
On the period of sequences in .
On the period of the continued fraction for values of the square root of power sums
On the possible orders of a basis for a finite cyclic group.
On the postage stamp problem with the three stamp denominations.
On the postage stamp problem with three stamp denominations, III.
On the postage stamp problem with three stamp denominations, II.
On the power values of Stirling numbers
On the prime density of Lucas sequences
The density of primes dividing at least one term of the Lucas sequence , defined by and for , with an arbitrary integer, is determined.