If (2021)^ 3762 is divided by 17, then the remainder is ........ - Vidyadip

Question

If $(2021)^{3762}$ is divided by $17$, then the remainder is ........

✓

Answer

c
$(2023-2)^{3762}=2023 k _{1}+2^{3762}$

$=17 k _{2}+2^{3762}($ as $2023=17 \times 17 \times 9)$

$=17 k _{2}+4 \times 16^{940}$

$=17 k _{2}+4 \times(17-1)^{940}$

$=17 k _{2}+4\left(17 k _{3}+1\right)$

$=17 k +4 \Rightarrow$ remainder $=4$

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