If the remainder when x is divided by 4 is 3, then the remainder when (2020 + x)^(2022) is divided by 8 is __________.

Let x = 4k + 3(2020 + x)^(2022)= (2020 + 4k + 3)^(2022)= (4(505) + 4k + 3)^(2022) = (4P + 3)^(2022)= (4P + 4 - 1)^(2022)= (4A - 1)^(2022)^(2022)C_(0)(4A)^(0)(-1)^(2022) + ^(2022)C_(1)(4A)^(1)(-1)^(2021) + ...... = 1 + 2022(4A)(-1) + ..... = 1 + 8lambda Therefore Reminder is 1.

If the remainder when x is divided by 4 is 3 then the r... | (Mathematics)

Let x = 4k + 3

(2020 + x)²⁰²²

= (2020 + 4k + 3)²⁰²²

= (4(505) + 4k + 3)²⁰²²

= (4P + 3)²⁰²²

= (4P + 4 $-$ 1)²⁰²²

= (4A $-$ 1)²⁰²²

²⁰²²C₀(4A)⁰( $-$ 1)²⁰²² + ²⁰²²C₁(4A)¹( $-$ 1)²⁰²¹ + ......

= 1 + 2022(4A)(-1) + .....

= 1 + 8 $\lambda$

$\therefore$ Reminder is 1.

Explanation

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