Exploració per autor "Cilleruelo, Javier"
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On a question of Sárkozy and Sós for bilinear forms
Cilleruelo, Javier; Rué Perna, Juan José (2009-02-02)
Article
Accés restringit per política de l'editorialWe prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers such that the representation function r(n)=#{(a, a'): n=$k{_1}a$ + $k{_2}a'$, a,a' ∊ $\emph{A}$} is constant for n large ... -
On monochromatic solutions of equations in groups
Cameron, Peter J.; Cilleruelo, Javier; Serra Albó, Oriol (2006-01-12)
Article
Accés obertResum no disponible -
On the fractional Parts of a^n/n
Cilleruelo, Javier; Luca, Florian; Kumchev, Angel; Rué Perna, Juan José; Shparlinski, Igor (2013-09-30)
Article
Accés obertWe give various results about the distribution of the sequence {a n/n}n=1 modulo 1, where a = 2 is a fixed integer. In particular, we find and infinite subsequence A such that {a n/n}n¿A is well distributed. Also we show ... -
On the number of nonzero digits of some integer sequences
Cilleruelo, Javier; Luca, Florián; Rué Perna, Juan José; Zumalacárregui, Ana (2012-06-05)
Article
Accés obertLet b = 2 be a fixed positive integer. We show for a wide variety of sequences {an}8n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence -
Set systems with distinct sumsets
Cilleruelo, Javier; Serra Albó, Oriol; Wötzel, Maximilian (Elsevier, 2018)
Text en actes de congrés
Accés obertA family $\mathcal{A}$ of $k$-subsets of $\{1,2,\dots, N\}$ is a Sidon system if the sumsets $A+A'$, $A,A'\in \mathcal{A}$ are pairwise distinct. We show that the largest cardinality $F_k(N)$ of a Sidon system of $k$-subsets ... -
Sidon set systems
Cilleruelo, Javier; Serra Albó, Oriol; Wötzel, Maximilian (2020-02-11)
Article
Accés obertA family A of k-subsets of {1,2,…,N} is a Sidon system if the sumsets A+B, A,B¿A are pairwise distinct. We show that the largest cardinality Fk(N) of a Sidon system of k-subsets of [N] satisfies Fk(N)=(N-1k-1)+N-k and the ... -
The least common multiple of random sets of positive integers
Cilleruelo, Javier; Rué Perna, Juan José; Sarka, Paulius; Zumalacárregui, Ana (2014-11-01)
Article
Accés obertWe study the typical behavior of the least common multiple of the elements of a random subset A¿{1,…,n}. For example we prove that lcm{a:a¿A}=2n(1+o(1)) for almost all subsets A¿{1,…,n}