What is the remainder when 5^{99} is divided by 13?
- A. 10
- B. 9
- C. 8 ✓
- D. 6
Correct Answer: C. 8
Explanation
By Fermat's Little Theorem, 5^{12} \equiv 1 \pmod{13}. We can express 99 = 12 \times 8 + 3. Thus, 5^{99} = (5^{12})^8 \cdot 5^3 \equiv 1^8 \cdot 125 \pmod{13}. Since 125 = 13 \times 9 + 8, the remainder is 8.
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