Carlip, Walter; Jacobson, Eliot A criterion for stability of two-term recurrence sequences modulo \(2^k\). (English) Zbl 0924.11007 Finite Fields Appl. 2, No. 4, 369-406 (1996). Let \(a\) and \(b\) be fixed integers and let \(\{u_i\), \(i\geq 0\}\) be the two-term recurrence sequence defined by \(u_0=0\), \(u_1=1\), and for all \(i\geq 2: u_i= au_{i-1}+ bu_{i-2}\). A new and interesting technique for characterizing stable sequences of the above type is described, where \(a\) is odd, \(b\equiv 3\pmod 4\). This technique is applied to identify stable sequences that were not previously known to be stable. Reviewer: K.Atanassov (Sofia) Cited in 4 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11B50 Sequences (mod \(m\)) Keywords:Fibonacci numbers; recurrence sequence; stable sequences PDFBibTeX XMLCite \textit{W. Carlip} and \textit{E. Jacobson}, Finite Fields Appl. 2, No. 4, 369--406 (1996; Zbl 0924.11007) Full Text: DOI