# If is divided by 17 , then the remainder is _______________. Option: 1 1 Option: 2 2 Option: 3 3 Option: 4 4

Divide 2021 by 17 we get -2 as remainder

\begin{aligned} (2023-2)^{3762}&=2023 k _{1}+2^{3762} \\ &=17 k _{2}+2^{3762}(\text { 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 \text { remainder }=4 \end{array}

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