Bases in which some numbers have exactly two expansions
نویسندگان
چکیده
منابع مشابه
On the Expansions of Real Numbers in Two Integer Bases
Let r ≥ 2 and s ≥ 2 be distinct integers. We establish that, if r and s are multiplicatively independent, then the r-ary expansion and the s-ary expansion of an irrational real number, viewed as infinite words on {0, 1, . . . , r− 1} and {0, 1, . . . , s− 1}, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words. We also discuss the c...
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Introduction. A long-standing problem in group theory is to determine the number of non-isomorphic groups of a given order. The inverse problem–determining the orders for which there are a given number of groups–has received considerably less attention. In this note, we will give a characterization of those positive integers n for which there exist exactly 2 distinct groups of order n (up to is...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.06.004