Competition problem — Number theory

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Number theory Difficulty 4.8 AIME Prove it United States

Problem:

Do there exist positive integers $x$ , $y$ , and $z$ such that $x^{2006} + y^{2006} = z^{2007}$ ? Explain your answer.

Solution

Solution:

Yes, for example, $x = y = z = 2$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.