Divisibility of the central binomial coefficient (2nn)

Kevin Ford, Sergei Konyagin

Research output: Contribution to journalArticlepeer-review

Abstract

We show that for every fixed l ∈ N, the set of n with nl|(2nn) has a positive asymptotic density cl and we give an asymptotic formula for cl as l → ∞. We also show that #{n ≼ x, (n, (2nn)) = 1} ∼ cx/ log x for some constant c. We use results about the anatomy of integers and tools from Fourier analysis. One novelty is a method to capture the effect of large prime factors of integers in general sequences.

Original languageEnglish (US)
Pages (from-to)823-953
Number of pages131
JournalTransactions of the American Mathematical Society
Volume374
Issue number2
DOIs
StatePublished - Feb 2021

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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