MathDB

Sum of digits problem

Source: 44th International Tournament of Towns, Junior A-Level P6, Fall 2022

February 16, 2023

number theorysum of digitsTournament of Towns

Problem Statement

Peter added a positive integer

M{}

to a positive integer

N{}

and noticed that the sum of the digits of the resulting integer is the same as the sum of the digits of

N{}

. Then he added

M{}

to the result again, and so on. Will Peter eventually get a number with the same digit sum as the number

N{}

again?