MathDB

Sum of Digits

Source: 2012 Paper 2 Problem 1

February 16, 2018

number theory

Problem Statement

Let

S(n)

be the sum of the decimal digits of

n

. For example.

S(2012)=2+0+1+2=5

. Prove that there is no integer

n>0

for which

n-S(n)=9990