Geodesic
The greatest common divisor of two recursive functions
Journal of integer sequences, Tome 7 (2004) no. 1
Let g, h be solutions of a linear recurrence relation of length 2. We show that under some mild assumptions the greatest common divisor of $g(n)$ and $h(n)$ is periodic as a function of $n$ and compute its mean value.
Classification : 11B37, 11B39, 11A05
Keywords: greatest common divisor, recursive functions, periodic functions, mean values 
@article{JIS_2004__7_1_a6,
     author = {Schlage-Puchta,  Jan-Christoph and Spilker,  J\"urgen},
     title = {The greatest common divisor of two recursive functions},
     journal = {Journal of integer sequences},
     year = {2004},
     volume = {7},
     number = {1},
     zbl = {1069.11002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a6/}
}
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Schlage-Puchta,  Jan-Christoph; Spilker,  Jürgen. The greatest common divisor of two recursive functions. Journal of integer sequences, Tome 7 (2004) no. 1. http://geodesic.mathdoc.fr/item/JIS_2004__7_1_a6/