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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
##### Keywords:
uniform distribution; recurrence
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