30 citations · 73 across the 25 of their papers we have counts for
22 papers · 1 filter
Every positive integer is a sum of three palindromes
Javier Cilleruelo, Florian Luca, Lewis Baxter
For integer , we prove that any positive integer can be written as a sum of three palindromes in base .
Visible lattice points in random walks
Javier Cilleruelo, José L. Fernández, Pablo Fernández
We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability and , respectively) and starting from the…
On sets free of sumsets with summands of prescribed size
Javier Cilleruelo, Rafael Tesoro
We study extremal problems about sets of integers that do not contain sumsets with summands of prescribed size. We analyse both finite sets and infinite sequences. We also study th…
On the congruence
Javier Cilleruelo, Moubariz Z. Garaev
In the present paper we obtain several new results related to the problem of upper bound estimates for the number of solutions of the congruence $$ x^{x}\equiv λ\pmod p;\quad x\in…
Additive properties of sequences of pseudo s-th powers
Javier Cilleruelo, Jean-Marc Deshouillers, Victor Lambert +1
In this paper, we study (random) sequences of pseudo s-th powers, as introduced by Erdös and Rényi in 1960. In 1975, Goguel proved that such a sequence is almost surely not an asym…
Gaps in sumsets of pseudo s-th power sequences
Javier Cilleruelo, Jean-Marc Deshouillers
We study the length of the gaps between consecutive members in the sumset sA when A is a pseudo s-th power sequence, with s>1. We show that, almost surely, limsup (b_{n+1}-b_{n})/l…