4 problems

A base-$g$ Niven number is a natural number divisible by the sum of its base-$g$ digits. A set of integers is an asymptotic basis of order $k$ if every sufficiently large natural n…

Digit-sum exception conjecture. No exceptions exist beyond the repdigit PINNs, the trivial PINNs $a0_{(0)}$ with $a\in\{1,2,3,4,5,6,7,8,9\}$, and the PINNs whose digit sums satisfy…

Repdigit Niven-number parametrization conjecture. The solutions of the repdigit Niven-number equation are parameterized by

Let $g\geq 2$ be an integer. A natural number is a base-$g$ Niven number if it is divisible by the sum of its base-$g$ digits. For an integer $a$, Hooley's Riemann Hypothesis (…