What is the remainder when 2^{p}-1 is divided by p, where p\gt 5 is a prime number?
- A. 1 ✓
- B. 2
- C. 3
- D. 4
Correct Answer: A. 1
Explanation
By Fermat's Little Theorem, 2^{p-1} \equiv 1 \pmod p. Multiplying by 2 gives 2^p \equiv 2 \pmod p. Therefore, (2^p - 1) \equiv 2 - 1 = 1 \pmod p. The remainder is 1.
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