• 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'editorial
      We 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 obert
      Resum 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 obert
      We 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 obert
      Let 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 obert
      A 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 obert
      A 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 obert
      We 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}