QJEEM22Ma5ec8: JEE Main 2022 Mathematics - Class 11 JEEM22Ma5ec8 Solution: The remainder when ( 2021 ) 2022 + ( 2022 ) 2021 is divided by…

Question

Verified Solution • 2025–26 Session moderate

The remainder when $(2021)^{2022} + (2022)^{2021}$ is divided by 7 is

Accepted Answer

$(2021)^{2022} + (2022)^{2021}$

$= (7 k - 2)^{2022} + (7 k_{1} - 1)^{2021}$

$= {[{(7 k - 2)}^{3}]}^{674} + (7 k_{1})^{2021} - 2021 (7 k_{1})^{2020} + . . . . - 1$

$= (7 k_{2} - 1)^{674} + (7 m - 1)$

$= (7 n + 1) + (7 m - 1) = 7 (m + n)$ (multiple of 7)

$∴$ Remainder = 0

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