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United States competition problems

Number theory Difficulty 5.0 AIME, harder Prove it United States

Problem:
Find all ordered pairs $(m, n)$ of integers such that $231 m^{2} = 130 n^{2}$ .

Solution

Solution:
The unique solution is $(0, 0)$ .

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