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Integer parts of powers of rational numbers

✍ Scribed by Artūras Dubickas; Aivaras Novikas


Publisher
Springer-Verlag
Year
2005
Tongue
French
Weight
194 KB
Volume
251
Category
Article
ISSN
0025-5874

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📜 SIMILAR VOLUMES


On the powers of 3/2 and other rational
✍ Artūras Dubickas 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB

## Abstract Let__p__ > __q__ > 1 be two coprime integers. In this paper, we prove several results about subsets of the interval [0, 1) which does or does not contain all the fractional parts {__ξ__ (__p__ /__q__)^__n__^ }, __n__ = 0, 1, 2, …, for certain non‐zero real number __ξ__. We show, for ins

A diophantine definition of integers in
✍ Alexandra Shlapentokh 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 568 KB

## Abstract The author considers rings of rational numbers which are integral at all the primes except, possibly, primes contained in a finite set. In such rings a Diophantine definition of ℤ is constructed to show that all the recursively enumerable subsets of the ring are Diophantine.