Stability of second-order recurrences modulo \(p^r\) (Q1567215)

This paper concerns congruence properties of binary linear recurrences \((\text{mod } p^r)\), where \(p\) is an odd prime. Such a recurrence is called ``\(p\)-stable'' if the set of frequencies of the distinct least positive residues \((\text{mod } p^r)\) is eventually constant as a function of \(r\). The authors develop sufficient conditions to determine whether certain binary linear recurrences are \(p\)-stable.