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UPSC CDS 2 2020 Math Paper

Question : 11 of 100

Marks: +1, -0

17^{2020}

is divided by 18, then what is the remainder?

Solution:

Concept:

Use the binomial expansion of

(18 - 1)^{2020}

to find the remainder when divided by 18.

Explanation:

Write

17

18 - 1

Then

17^{2020} = (18 - 1)^{2020}

By the binomial theorem, all terms except the last contain a factor of

18

and are divisible by

18

The last term is

(-1)^{2020} = 1

Therefore,

17^{2020} = 18 \times (\text{some integer}) + 1

Hence, when divided by

18

, the remainder is

1

Answer:

A. 1

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