A lower bound for the quantity \(\| (3/2)^ k\|\). (English. Russian original) Zbl 0712.11037

Russ. Math. Surv. 45, No. 4, 163-164 (1990); translation from Usp. Mat. Nauk 45, No. 4(274), 153-154 (1990).
An effective result is proved for showing that \((3/2)^ k\) cannot be too close to an integer. Improving a result of F. Beukers [Math. Proc. Camb. Philos. Soc. 90, 13–20 (1981; Zbl 0466.10030)] the author proves \(\| (3/2)^ k\| >(0.5769)^ k\) for \(k\) large enough. The proof is similar to that of Beukers.
Reviewer: A. Balog


11J71 Distribution modulo one
11J04 Homogeneous approximation to one number


Zbl 0466.10030
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