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Niven repunits in general bases. (English) Zbl 1400.11009
Summary: We show that the generalized repunit $$(b^n-1)/(b-1)$$ is divisible by $$n$$ if and only if $$n$$ is divisible by the multiplicative order of $$b$$ modulo every prime factor of $$n$$. This fact is a generalization of an older result which holds for $$b=10$$. A few consequences of this theorem concerning base-$$b$$ Niven numbers are also discussed.
##### MSC:
 11A07 Congruences; primitive roots; residue systems 11A63 Radix representation; digital problems
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