Walter Carlip, Department of Mathematics, Franklin & Marshall College, Lancaster, Pennsylvania 17604, USA; mailing address: 408 Harvard Street, Vestal, New York 13850, USA, e-mail: email@example.com; Lawrence Somer, Department of Mathematics, Catholic University of America, Washington D. C. 20064, USA, e-mail: firstname.lastname@example.org
Abstract: The authors examine the frequency distribution of second-order recurrence sequences that are not $p$-regular, for an odd prime $p$, and apply their results to compute bounds for the frequencies of $p$-singular elements of $p$-regular second-order recurrences modulo powers of the prime $p$. The authors' results have application to the $p$-stability of second-order recurrence sequences.
Keywords: Lucas, Fibonacci, stability, uniform distribution, recurrence
Classification (MSC2000): 11B37, 11A25, 11A51, 11B39
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