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JEE Main 202117 MarchMorning Shift

Exam: JEE Main
Year: 2021
Date: 17 March
Shift: Morning Shift
Subject: Mathematics
Chapter: Binomial Theorem

JEE Main 2021 · 17 March · Morning Shift · Mathematics · Binomial Theorem

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

If

( 2021{)}^{3762}

is divided by

17,

then the remainder is _______.

Correct answer

0

Step-by-step solution

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

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

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

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

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

$= 17k + 4 ⇒$ remainder $= 4$

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