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arXiv · 1807.02573

High degree $b$-Niven numbers

Viorel Nitica
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Abstract

Let $b$ be a numeration base. A $b$-Niven number is one that is divisible by the sum of its base $b$ digits. We introduce high degree $b$-Niven numbers. These are $b$-Niven numbers that have a power greater than $1$ that is $b$-Niven number. Our main result shows that for each degree there exists an infinite set of bases $b$ for which $b$-Niven numbers of that degree exist. The high degree $b$-Niven numbers are given by explicit formulas and have all digits different from zero.

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Viorel Nitica. 2018-07-06. High degree $b$-Niven numbers. https://arxiv.org/abs/1807.02573

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