Sums of Niven numbers via the circle method

A base-g Niven number is an integer divisible by its base-g digit sum. In this talk, we will show that, for any g\geq 3, all sufficiently large integers are the sum of three base-g Niven numbers. The proof uses the circle method, which we also use to count the number of ways to write an integer as the sum of three integers with certain fixed digit sums.