MathDB

On the multiple and sum of digits

Source: 2022 Thailand MO Day 2 P10

June 16, 2022

number theory

Problem Statement

For each positive integers

u

and

n

, say that

u

is a friend of

n

if and only if there exists a positive integer

N

that is a multiple of

n

and the sum of digits of

N

(in base 10) is equal to

u

. Determine all positive integers

n

that only finitely many positive integers are not a friend of

n