JEE MAIN - Mathematics (2024 - 29th January Evening Shift - No. 28)
Remainder when $$64^{32^{32}}$$ is divided by 9 is equal to ________.
Answer
1
Explanation
Let $$32^{32}=\mathrm{t}$$
$$\begin{aligned} & 64^{32^{32}}=64^t=8^{2 t}=(9-1)^{2 t} \\ & =9 \mathrm{k}+1 \end{aligned}$$
Hence remainder $$=1$$
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