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Moscow Mathematical Journal

Volume 21, Issue 1, January–March 2021  pp. 31–42.

On the Zeckendorf Representation of Smooth Numbers

Authors:  Yann Bugeaud (1)
Author institution:(1) Institut de Recherche Mathématique Avancée, U.M.R. 7501, Université de Strasbourg et C.N.R.S., 7, rue René Descartes, 67084 Strasbourg, FRANCE


Among other results, we establish, in a quantitative form, that any sufficiently large integer cannot simultaneously be divisible only by very small primes and have very few digits in its Zeckendorf representation.

2010 Math. Subj. Class. 11A63, 11J86, 11N25.

Keywords: Radix representation, Baker's theory, Schmidt Subspace Theorem.

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