4

Part of 2006 Estonia Math Open Junior Contests

Problems(1)

Estonian Math Competitions 2005/2006

Source: Juniors Problem 3

Does there exist a natural number with the sum of digits of its

kth

power being equal to

k

, if a) k \equal{} 2004; b) k \equal{} 2006?

number theoryrelatively primenumber theory unsolved