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arXiv · 2511.02790

Niven numbers are an asymptotic basis of order 3

Kate Thomas
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Abstract

A base-$g$ Niven number is a natural number divisible by the sum of its base-$g$ digits. We show that, for any $g\geq 3$, all sufficiently large natural numbers can be written as the sum of three base-$g$ Niven numbers. We also give an asymptotic formula for the number of representations of a sufficiently large integer as the sum of three integers with fixed, close to average, digit sums.

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Kate Thomas. 2025-11-04. Niven numbers are an asymptotic basis of order 3. https://arxiv.org/abs/2511.02790

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