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
Gaps in dense Sidon sets.
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.
On multiplicative magic squares.
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