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Characterization of the unique expansions $$1=\sum^{\infty}_{i=1}q^{-n_ i}$$ and related problems. (English) Zbl 0721.11005
Given a nonintegral base $$1<q<2$$, the authors characterize the expansions of 1 base $$q$$ for which uniqueness holds. Estimates for the number of consecutive zero digits in the greedy expansion of 1 are also obtained. These results are related to the sequence of real numbers which has finite base $$q$$ expansions. Some open problems are given at the end of the article.

##### MSC:
 11A67 Other number representations
Full Text:
##### References:
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