Additive bases and Niven numbers

Carlo Sanna

Published 2021-01-19Version 1

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 for $g$, we prove that the set of base-$g$ Niven numbers is an additive basis, that is, there exists $C_g > 0$ such that every natural number is the sum of at most $C_g$ base-$g$ Niven numbers.