Maths Olympiad Prep

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Algebra Difficulty 4.7 AIME Find the answer

Find all ordered pairs (m,n)(m, n) of integers such that 231m2=130n2231 m^{2}=130 n^{2}.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

The unique solution is (0,0)(0,0).

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Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.