JEE Mains · Maths · STD 11 - 7. binomial theoram
If \((2021)^{3762}\) is divided by \(17\), then the remainder is ........
- A \(9\)
- B \(12\)
- C \(4\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\((2023-2)^{3762}=2023 k _{1}+2^{3762}\) \(=17 k _{2}+2^{3762}(\) 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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