The remainder when 3^{2022} is divided by 5 i | vedclass

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(D) We need to find the remainder of $3^{2022}$ when divided by $5$.$3^{2022} = (3^2)^{1011} = 9^{1011}$.We can write $9$ as $(10 - 1)$.So,$9^{1011} =

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$4$

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(D) We need to find the remainder of $3^{2022}$ when divided by $5$.$3^{2022} = (3^2)^{1011} = 9^{1011}$.We can write $9$ as $(10 - 1)$.So,$9^{1011} = (10 - 1)^{1011}$.Using the Binomial Theorem,$(10 - 1)^{1011} = \sum_{k=0}^{1011} \binom{1011}{k} 10^{1011-k} (-1)^k$.This can be written as $10 \cdot N + (-1)^{1011}$,where $N$ is an integer.$10 \cdot N - 1 = 10 \cdot N - 5 + 4 = 5(2N - 1) + 4$.Therefore,the remainder when $3^{2022}$ is divided by $5$ is $4$.

The remainder when $3^{2022}$ is divided by $5$ is

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