294

Part of 1980 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 294 All Soviet Union MO 1980 n+S(n)=1980, sum of digits

Source:

Let us denote with

S(n)

the sum of all the digits of

n

.
a) Is there such an

n

n+S(n)=1980

?
b) Prove that at least one of two arbitrary successive natural numbers is representable as

n + S(n)

for some third number

n

sum of digitsnumber theory