Gaps in dense Sidon sets.
On multiplicative magic squares.
Arcs containing no three lattice points
El sistema binario.
Cuadrados mágicos.
Conjuntos de enteros con todas las diferencias distintas.
Progresiones aritméticas en sucesiones de enteros.
La conjetura de Goldbach.
B₂[∞]-sequences of square numbers
On the largest prime factor of the partition function of n
An overlapping theorem with applications.
We establish a general and optimal lower bound for the complete sum of the probabilities of k-intersections of n events. We then describe various applications to additive and multiplicative number theory, graph theory, coding theory, study of lattice points on circles, and divisors of polynomials.
[Proceedings of the
The hyperbola
We include several results providing bounds for an interval on the hyperbola containing lattice points.
Divisors in a Dedekind domain
On the sum of digits of some sequences of integers
Let b ≥ 2 be a fixed positive integer. We show for a wide variety of sequences {a n}n=1∞ that for almost all n the sum of digits of a n in base b is at least c b log n, where c b is a constant depending on b and on the sequence. Our approach covers several integer sequences arising from number theory and combinatorics.
Page 1