Journal of Integer Sequences, Vol. 13 (2010), Article 10.2.4 |

Chris Smyth

School of Mathematics and Maxwell Institute for Mathematical Sciences

University of Edinburgh

James Clerk Maxwell Building

King's Buildings

Mayfield Road

Edinburgh EH9 3JZ

United Kingdom

**Abstract:**

For Lucas sequences of the first kind
and second kind
defined as usual by
,
, where and are either integers or
conjugate quadratic integers, we describe the sets
divides and
divides .
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 , or , 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.

(Concerned with sequences A006521 A014662 A016089 A023172 A057719 A091317 A129729 A140409.)

Received August 21 2009;
revised version received January 29 2010.
Published in *Journal of Integer Sequences*, January 31 2010.

Return to