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Bundeswettbewerb Mathematik 1978 Problem 1.3

Source: Bundeswettbewerb Mathematik 1978 Round 1

October 12, 2022
number theoryDivisionSumpower of 2

Problem Statement

For every positive integer nn, define the remainder sum r(n)r(n) as the sum of the remainders upon division of nn by each of the numbers 11 through nn. Prove that r(2k−1)=r(2k)r(2^{k}-1) =r(2^{k}) for every k≥1.k\geq 1.
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