MathDB

5

Part of 1996 Swedish Mathematical Competition

Problems(1)

equal sum of the $p$-th powers of numbers from 1,2,...,2^n

Source: 1996 Swedish Mathematical Competition p5

4/2/2021
Let n≥1n \ge 1. Prove that it is possible to select some of the integers 1,2,...,2n1,2,...,2^n so that for each p=0,1,...,n−1p = 0,1,...,n - 1 the sum of the pp-th powers of the selected numbers is equal to the sum of the pp-th powers of the remaining numbers.
number theorypower of 2Sum of powers