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The remainder when 4282024 is divided by 21 is | null (Mathematics) | DivineJEE

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Mathematics

Exam

Mathematics

The remainder when $428^{2024}$ is divided by 21 is __________.

Correct Answer:

1

Explanation

\begin{aligned} & 428=21 \times 20+8 \\ \Rightarrow \quad & (428)^{2024} \equiv(20 \times 21+8)^{2024} \equiv 8^{2024}(\bmod 21) \\ & 8^2=21 \times 3+1 \\ & 8^{2024}=(21 \times 3+1)^{1012} \\ \Rightarrow \quad & 8^{2024} \equiv(21 \times 3+1)^{1012}(\bmod 21) \\ & \equiv 1^{2012}(\bmod 21) \\ & 428^{2024} \equiv 1(\bmod 21) \end{aligned}

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