Kate Thomas

Sums of integers divisible by the sum of their digits

A base-g Niven number is an integer divisible by the sum of its digits in base-g. We show that any sufficiently large integer can be written as the sum of three base-3 Niven numbers. This follows from an application of the circle method, which we use to count the number of ways an integer can be written as the sum of three integers with fixed, near-average, digit sum.