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arXiv · 2101.07593

Additive bases and Niven numbers

Carlo Sanna
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Abstract

Let $g \geq 2$ be an integer. A natural number is said to be a base-$g$ Niven number if it is divisible by the sum of its base-$g$ digits. Assuming Hooley's Riemann Hypothesis, we prove that the set of base-$g$ Niven numbers is an additive basis, that is, there exists a positive integer $C_g$ such that every natural number is the sum of at most $C_g$ base-$g$ Niven numbers.

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Carlo Sanna. 2021-01-19. Additive bases and Niven numbers. https://doi.org/10.1017/s0004972721000186

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