MathDB

Let

n

be a positive integer; and

S(n)

denote the sum of all digits in the decimal representation of

n

. A positive integer obtained by removing one or several digits from the right hand end of the decimal representation of

n

is called the truncation of

n

. The sum of all truncations of

n

is denoted as

T(n)

. Prove that

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

Problem Statement