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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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