2014/02/04 by Jeremiah T. Southwick, Southwick, Jeremiah T.
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1402.0598
arxiv created 2014/02/04 · arxiv updated 2014/02/05
We study Gibonacci sequences mod m, giving special attention to the Lucas numbers. It is known which m have the property that the Fibonacci sequence contains all residues mod m. When m has this property, we say that the Fibonacci sequence is complete mod m. We extend this work to all Gibonacci sequences, concluding by determining the set of m in which a generic Gibonacci sequence containing the relatively prime consecutive terms a, b is complete mod m.