Additive bases and Niven numbers

Abstract

Let $g\ge 2$ 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.

References in corpus (2)

• Vinogradov's three primes theorem with primes having given primitive roots
• On numbers divisible by the product of their nonzero base $b$ digits