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MR1078082 (91j:11006) 11A63 (11K55) Erdös, Pál; Joó, István; Komornik, Vilmos Characterization of the unique expansions $1=\sum\sp \infty\sb {i=1}q\sp {-n\sb i}$ and related problems. Bull. Soc. Math. France 118 (1990), no. 3, 377--390.

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