Additive bases and Niven numbers

TL;DR

Under the assumption of Hooley's Riemann Hypothesis, the paper proves that base-$g$ Niven numbers form an additive basis, meaning every natural number can be expressed as a sum of a bounded number of such numbers.

Contribution

It establishes, assuming a major unproven hypothesis, that base-$g$ Niven numbers can generate all natural numbers through bounded sums.

Findings

The set of base-$g$ Niven numbers is an additive basis under Hooley's Riemann Hypothesis.

Every natural number can be expressed as a sum of at most $C_g$ base-$g$ Niven numbers.

The result links number divisibility properties with additive number theory under a deep hypothesis.

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.