Geodesic
Bounds for frequencies of residues of second-order recurrences modulo $p^r$
Mathematica Bohemica, Tome 132 (2007) no. 2, pp. 137-175.

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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.
DOI : 10.21136/MB.2007.134189
Classification : 11A25, 11A51, 11B37, 11B39, 11B50
Keywords: Lucas; Fibonacci; stability; uniform distribution; recurrence 
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Carlip, Walter; Somer, Lawrence. Bounds for frequencies of residues of second-order recurrences modulo $p^r$. Mathematica Bohemica, Tome 132 (2007) no. 2, pp. 137-175. doi : 10.21136/MB.2007.134189. http://geodesic.mathdoc.fr/articles/10.21136/MB.2007.134189/

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