Glasnik Matematicki, Vol. 44, No.2 (2009), 285-307.

ARITHMETIC PROPERTIES OF THE INTEGER PART OF THE POWERS OF AN ALGEBRAIC NUMBER

Florian Luca and Maurice Mignotte

Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México
e-mail: fluca@matmor.unam.mx

Université Louis Pasteur, UFR de mathématiques, 7 rue René Descartes, 67084 Strasbourg, France
e-mail: mignotte@math.u-strasbg.fr


Abstract.   For a real number x, we let [x] be the closest integer to x. In this paper, we look at the arithmetic properties of the integers [θn] when n ≥ 0, where θ > 1 is a fixed algebraic number.

2000 Mathematics Subject Classification.   11D45, 11D75.

Key words and phrases.   Powers of algebraic numbers, digital representations, applications of linear forms in logarithms and the subspace theorem.


Full text (PDF) (free access)

DOI: 10.3336/gm.44.2.03


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