Aspire Faculty ID #13876 · Topic: JAMIA MILLIA ISLAMIA MCA 2021 · Just now
JAMIA MILLIA ISLAMIA MCA 2021

If $x$, when divided by 4, leaves remainder 3, then find the remainder when $(2020 + x)^{2022}$ is divided by 8.

Solution

Then $2020 + x = 2020 + 4k + 3 = 4k + 2023$ 
Now $2020 \equiv 4 \pmod{8} $
$\Rightarrow 2020 + x \equiv 4 + 3 = 7 \pmod{8}$ 
So $(2020 + x)^{2022} \equiv 7^{2022} \pmod{8}$ 
Since $7 \equiv -1 \pmod{8}$, $(-1)^{2022} = 1$. 
Hence remainder = 1.
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