MathDB

1

Part of 2001 APMO

Problems(1)

Sum of digits

Source: APMO 2001

3/19/2006
For a positive integer nn let S(n)S(n) be the sum of digits in the decimal representation of nn. Any positive integer obtained by removing several (at least one) digits from the right-hand end of the decimal representation of nn is called a stump of nn. Let T(n)T(n) be the sum of all stumps of nn. Prove that n=S(n)+9T(n)n=S(n)+9T(n).
inductionnumber theoryeasy