MathDB

142

Part of 1970 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 142 All Soviet Union MO 1970 even sum of digits, odd sum of digits

Source:

6/24/2019
All natural numbers containing not more than nn 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 0<k<n0<k<n than the sum of the kk-th powers of the numbers in the first group equals to the sum of the kk-th powers of the numbers in the second group.
number theoryDigits