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A criterion for stability of two-term recurrence sequences modulo \(2^k\). (English) Zbl 0924.11007

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.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11B50 Sequences (mod \(m\))
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