International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 225-241

Stability of second-order recurrences modulo pr

Lawrence Somer1 and Walter Carlip2

1Department of Mathematics, Catholic University of America, Washington 20064, DC, USA
2Department of Mathematics, Duke University, Durham 27708, North Carolina, USA

Received 13 April 1999

Copyright © 2000 Lawrence Somer and Walter Carlip. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p-stable if the set of residue frequencies of the sequence reduced modulo pr is eventually constant as a function of r. The authors identify and characterize the stability of second-order recurrences modulo odd primes.