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

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.

DOI: 10.3336/gm.44.2.03

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