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ASU 499 All Soviet Union MO 1989 2 reals with sum of nth powers irrational

Source:

August 13, 2019
irrationalSumSum of powersrationalalgebra

Problem Statement

Do there exist two reals whose sum is rational, but the sum of their nn th powers is irrational for all n>1n > 1? Do there exist two reals whose sum is irrational, but the sum of whose nn th powers is rational for all n>1n > 1?
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