The Terms in Lucas Sequences Divisible by Their Indices

Christopher Smyth

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

For Lucas sequences of the first kind (u_n) and second kind (v_n) defined as usual for positive n by u_n=(a^n-b^n)/(a-b), v_n=a^n+b^n, where a and b are either integers or conjugate quadratic integers, we describe the set of indices n for which n divides u_n and also the set of indices n for which n divides v_n. Building on earlier work, particularly that of Somer, we show that the numbers in these sets can be written as a product of a so-called basic number, which can only be 1, 6 or 12, and particular primes, which are described explicitly. Some properties of the set of all primes that arise in this way is also given, for each kind of sequence.
Original languageEnglish
Article number10.2.4
Number of pages18
JournalJournal of Integer Sequences
Volume13
Issue number2
Early online date31 Jan 2010
Publication statusPublished - 2010

Keywords / Materials (for Non-textual outputs)

  • Lucas sequences
  • indices

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