MathDB

For a positive integer

n

let

S(n)

be the sum of digits in the decimal representation of

n

. Any positive integer obtained by removing several (at least one) digits from the right-hand end of the decimal representation of

n

is called a stump of

n

. Let

T(n)

be the sum of all stumps of

n

. Prove that

n=S(n)+9T(n)

Problem Statement