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Weird inequality

Source: Kvant Magazine No. 3 2021 M2642

March 9, 2023

algebrainequalitiesKvant

Problem Statement

The nonzero numbers

x{}

and

y{}

satisfy the inequalities

x^{2n}-y^{2n}>x

and

y^{2n}-x^{2n}>y

for some natural number

n{}

. Can the product

xy

be a negative number?
Proposed by N. Agakhanov

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