Niven Repunits in General Bases
Amin Witno · The Fibonacci Quarterly · 2016
We show that the generalized repunit (bn - 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.