Niven numbers are an asymptotic basis of order 3
Abstract
A base-g Niven number is a natural number divisible by the sum of its base-g digits. We show that, for any g≥ 3, all sufficiently large natural numbers can be written as the sum of three base-g Niven numbers. We also give an asymptotic formula for the number of representations of a sufficiently large integer as the sum of three integers with fixed, close to average, digit sums.
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