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MATHEMATICA BOHEMICA, Vol. 132, No. 2, pp. 137-175 (2007)
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#
Bounds for frequencies of residues of

second-order recurrences modulo $p^r$

##
Walter Carlip, Lawrence Somer

* Walter Carlip*, Department of Mathematics, Franklin & Marshall College, Lancaster, Pennsylvania 17604, USA; mailing address: 408 Harvard Street, Vestal, New York 13850, USA, e-mail: ` c3ar@math.uchicago.edu`; * Lawrence Somer*, Department of Mathematics, Catholic University of America, Washington D. C. 20064, USA, e-mail: ` somer@cua.edu`

**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

**Full text of the article:**

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