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What is the remainder when (265)^4081 + 9 is divided by 266?

1. 8
2. 6
3. 1
4. 9

Correct answer: 8

Solution

Since 265 = 266 - 1, we have 265 ≡ -1 (mod 266). As 4081 is odd, (-1)^4081 = -1 ≡ 265 (mod 266). Adding 9: 265 + 9 = 274. 274 - 266 = 8. Remainder = 8.

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