The remainder when 7^{2022} + 3^{2022} is div | vedclass

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(C) We need to find the remainder of $7^{2022} + 3^{2022}$ when divided by $5$.Note that $7 \equiv 2 \pmod{5}$ and $3 \equiv -2 \pmod{5}$.Thus,$7^{202

Vedclass · Accepted Answer

$3$

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(C) We need to find the remainder of $7^{2022} + 3^{2022}$ when divided by $5$.Note that $7 \equiv 2 \pmod{5}$ and $3 \equiv -2 \pmod{5}$.Thus,$7^{2022} + 3^{2022} \equiv 2^{2022} + (-2)^{2022} \pmod{5}$.Since $2022$ is an even number,$(-2)^{2022} = 2^{2022}$.So,$7^{2022} + 3^{2022} \equiv 2^{2022} + 2^{2022} = 2 	imes 2^{2022} = 2^{2023} \pmod{5}$.We know that $2^4 = 16 \equiv 1 \pmod{5}$.Therefore,$2^{2023} = 2^{4 	imes 505 + 3} = (2^4)^{505} 	imes 2^3 \equiv 1^{505} 	imes 8 \equiv 8 \pmod{5}$.Finally,$8 \equiv 3 \pmod{5}$.The remainder is $3$.

The remainder when $7^{2022} + 3^{2022}$ is divided by $5$ is:

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