Powers of a rational number modulo 1 cannot lie in a small interval
نویسندگان
چکیده
منابع مشابه
Powers of rationals modulo 1 and rational base number systems
A new method for representing positive integers and real numbers in a rational base is considered. It amounts to computing the digits from right to left, least significant first. Every integer has a unique such expansion. The set of expansions of the integers is not a regular language but nevertheless addition can be performed by a letter-to-letter finite right transducer. Every real number has...
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This is a review of several results related to distribution of powers and combinations of powers modulo 1. We include a proof that given any sequence of real numbers n , it is possible to get an (given 6 = 0), or a (given > 1) such that n is close to n modulo 1. We also prove that in a number eld, if a combination of powers 1 n 1 + + m n m has bounded v-adic absolute value (where v is any non-A...
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Since 2 is a primitive root of 3 for each positive integer m, the set of points {(n, 2 mod 3) : n > 0}, viewed as a subset of Z>0×Z>0 is bi-periodic, with minimal periods φ(3) (horizontally) and 3 (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of...
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15 صفحه اولThe overpartition function modulo small powers of 2
In a recent paper, Fortin, Jacob and Mathieu [5] found congruences modulo powers of 2 for the values of the overpartition function p(n) in arithmetic progressions. The moduli for these congruences ranged as high as 64. This note shows that p(n) ≡ 0 (mod 64) for a set of integers of arithmetic density 1.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa137-3-4