  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.
