• Erdös y los enteros 

    Cilleruelo, Javier (2011-03-02)
    Audiovisual
    Accés obert
  • 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
  • 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}