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AIME 2005b Problem 7

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Let x=4(5+1)(54+1)(58+1)(516+1).x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}. Find (x+1)48(x+1)^{48}.

Dataset text AIME 1983 to 2026. Quoted with source.

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