CDS 2025 · PYQ · Number Theory / Fermat's Little Theorem · medium
What is the remainder when 2^p - 1 is divided by p, where p > 5 is a prime number?
- A.1✓ Correct
- B.2
- C.3
- D.4
By Fermat's Little Theorem, for prime p, 2^p ≡ 2 (mod p). So 2^p - 1 ≡ 2 - 1 ≡ 1 (mod p). The remainder is 1.
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