no. 3
Characterization of the unique expansions 1=∑ i=1 ∞ q -n i and related problems
Bulletin de la Société Mathématique de France, Tome 118 (1990) no. 3, pp. 377-390. 
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     author = {Erd\"os, P\'al and Jo\'o, Istv\'a n and Komornik, Vilmos},
     title = {Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {377--390},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {118},
     number = {3},
     year = {1990},
     doi = {10.24033/bsmf.2151},
     mrnumber = {91j:11006},
     zbl = {0721.11005},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/bsmf.2151/}
}
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Erdös, Pál; Joó, Istvá n; Komornik, Vilmos. Characterization of the unique expansions $1=\sum ^{\infty }_{i=1}q^{-n_ i}$ and related problems. Bulletin de la Société Mathématique de France, Tome 118 (1990) no. 3, pp. 377-390. doi : 10.24033/bsmf.2151. http://archive.numdam.org/articles/10.24033/bsmf.2151/

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[5] Erdös (P.), Horváth (M.) and Joó (I.). - On the uniqueness of the expansions 1 = Σq-ni, to appear.

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