Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

[48.5] Let $a$ and $b$ be positive integers. Given that $4ab-1$ divides $\left(4a^{2}-1\right)^{2}$ . Prove: $a=b$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.