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Bounds for frequencies of residues of second-order recurrences modulo \(p^r\). (English) Zbl 1174.11014
Summary: 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.

MSC:
11B37 Recurrences
11A25 Arithmetic functions; related numbers; inversion formulas
11A51 Factorization; primality
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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