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System of equations: hard

Source: Kyiv City MO 2024 Round 2, Problem 11.1

February 4, 2024
algebrasystem of equations

Problem Statement

Solve the following system of equations in real numbers: {x2=y2+z2,x2024=y2024+z2024,x2025=y2025+z2025.\left\{\begin{array}{l}x^2=y^2+z^2,\\x^{2024}=y^{2024}+z^{2024},\\x^{2025}=y^{2025}+z^{2025}.\end{array}\right. Proposed by Mykhailo Shtandenko, Anton Trygub, Bogdan Rublov
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