The remainder when 428^ 2024 is divided by 21 is ............ - Vidyadip

Question

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

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Answer

a
$ (428)^{2024}=(420+8)^{2024} $

$ =(21 \times 20+8)^{2024} $

$ =21 \mathrm{~m}+8^{2024} $

$ \text { Now } 8^{2024}=\left(8^2\right)^{1012} $

$ =(64)^{1012} $

$ =(63+1)^{1012} $

$ =(21 \times 3+1)^{1012} $

$ =21 \mathrm{n}+1 $

$ \Rightarrow \text { Remainder is } 1 .$

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