QJEEM24Ma1f03: JEE Main 2024 Mathematics - Class 11 JEEM24Ma1f03 Solution: Remainder when 64 32 32 is divided by 9 is equal to ________.

Question

Verified Solution • 2025–26 Session moderate

Remainder when $64^{32^{32}}$ is divided by 9 is equal to ________.

Accepted Answer

Let $32^{32} = t$

$\begin{aligned} 64^{32^{32}} = 64^{t} = 8^{2 t} = (9 - 1)^{2 t} \\ = 9 k + 1 \end{aligned}$

Hence remainder $= 1$

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