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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
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