What is the remainder when 2^{101} is divided by 101?
- A. 1
- B. 2 ✓
- C. 5
- D. 7
Correct Answer: B. 2
Explanation
Since 101 is a prime number, by Fermat's Little Theorem, a^{p-1} \equiv 1 \pmod p, so 2^{100} \equiv 1 \pmod{101}. Therefore, 2^{101} = 2^{100} \times 2 \equiv 1 \times 2 = 2 \pmod{101}.
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