The remainder when 2 2003 is divided by 17 is

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Question: Answered & Verified by Expert

The remainder when

2^{2003}

is divided by

17

is

MathematicsBinomial TheoremJEE Main

Options:

A $1$
B $2$
C $8$
D $11$

Solution:

1180 Upvotes Verified Answer

The correct answer is:

8

2^{2003} = 2^{3} 2^{2000} = 8 {(2^{4})}^{500}

= 8 {(16)}^{500} = 8 {(17 - 1)}^{500}

= 8 \{{{}^{500}C}_{0} \cdot 17^{500} - {{}^{500}C}_{1} \cdot 17^{499} + . \dots \dots . . - {{}^{500}C}_{499} \cdot 17 + {{}^{500}C}_{500}\}

= 8 (17 k + 1) = 8 \times 17 k + 8

So, the remainder obtained is

8

.

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