The remainder when (2021)^ 203 is divided by 7 is - Vidyadip

MCQ

The remainder when $(2021)^{203}$ is divided by $7$ is

A
$1$
B
$2$
✓
$5$
D
$6$

✓

Answer

Correct option: C.

$5$

c
$(2021)^{2023}=(7 \lambda-2)^{2023}$

$={ }^{2023} C_{0}(7 A )^{2023}-\ldots{ }^{2023} C _{2023} 2^{2023}$

$=7 t -2^{2023}$

$\therefore-2^{2023}=-2 \times 2^{2022}$

$=-2 \times\left(2^{3}\right)^{674}$

$=-2(1+7 \mu)^{674}$

$=-(7 \alpha+2)$

$\Rightarrow \text { remainder }=-2 \text { or }+5$

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