Corpus ID: 7670099

The Terms in Lucas Sequences Divisible by Their Indices

@inproceedings{Smyth2009TheTI,
  title={The Terms in Lucas Sequences Divisible by Their Indices},
  author={C. Smyth},
  year={2009}
}
For Lucas sequences of the first kind (un)n�0 and sec- ond kind (vn)n�0 defined as usual by un = (� n − � n )/(� − �), vn = � n +� n , whereandare either integers or conjugate qua- dratic integers, we describe the sets {n ∈ N : n divides un} and {n ∈ N : n divides vn}. 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… Expand
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