MathDB

IMO ShortList 1999, number theory problem 5

Source: IMO ShortList 1999, number theory problem 5

November 13, 2004

number theorydecimal representationsum of digitsIMO Shortlist

Problem Statement

Let

n,k

be positive integers such that n is not divisible by 3 and

k \geq n

. Prove that there exists a positive integer

m

which is divisible by

n

and the sum of its digits in decimal representation is

k