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What is the remainder when 19^200 is divided by 20?

1. 3
2. 1
3. -1
4. 2

Correct answer: 1

Solution

19 = (20 - 1). So 19^200 = (20-1)^200. By the binomial theorem, every term except (-1)^200 contains 20 as a factor. (-1)^200 = 1 (even power). Therefore, 19^200 mod 20 = 1.

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