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A criterion on multiples of generalized repunits. (English) Zbl 1346.11004
Summary: We prove that the sum of $$n$$ powers of $$b$$ is divisible by $$(b^n-1)/(b-1)$$ if and only if the $$n$$ exponents are all distinct modulo $$n$$. If $$b=10$$, this result is already known, and we present an alternate proof with this generalization.
##### MSC:
 11A07 Congruences; primitive roots; residue systems 11A63 Radix representation; digital problems
##### Keywords:
generalized repunits
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