ASU 142 All Soviet Union MO 1970 even sum of digits, odd sum of digits
Source:
June 24, 2019
number theoryDigits
Problem Statement
All natural numbers containing not more than digits are divided onto two groups. The first contains the numbers with the even sum of the digits, the second -- with the odd sum. Prove that if than the sum of the -th powers of the numbers in the first group equals to the sum of the -th powers of the numbers in the second group.