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Sum of odd powers is 0

Source: Kvant Magazine No. 11 2019 M2585*

March 14, 2023
algebraPolynomialsKvant

Problem Statement

Let a1,...,ana_1,...,a_n be nn real numbers. If for each odd positive integer k⩽nk\leqslant n we have a1k+a2k+…+ank=0a_1^k+a_2^k+\ldots+a_n^k=0, then for each odd positive integer kk we have a1k+a2k+…+ank=0a_1^k+a_2^k+\ldots+a_n^k=0.
Proposed by M. Didin
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