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Geometrization of the Fibonacci numeration system, with applications to number theory. (English. Russian original) Zbl 1369.11013
St. Petersbg. Math. J. 25, No. 6, 893-907 (2014); translation from Algebra Anal. 25, No. 6, 1-23 (2013).
Summary: A geometrization theorem is obtained for the Fibonacci numeration system. As applications, several classical problems are solved concerning numbers that have a given tail of the expansion with respect to the Fibonacci numeration system.

MSC:
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11A67 Other number representations
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