olymmath

HMMT 2008 U17

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  • Answer

Solve the equation

x+4x+16x+…+42008x+3−x=1\sqrt{x+\sqrt{4 x+\sqrt{16 x+\sqrt{\ldots+\sqrt{4^{2008} x+3}}}}}-\sqrt{x}=1

Express your answer as a reduced fraction with the numerator and denominator written in their prime factorization.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{1}{2^{4016}}

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