CDS 2025 · PYQ · Number Theory / Fermat's Little Theorem · medium
What is the remainder when 2^101 is divided by 101?
Answer
The correct answer is B: 2. By Fermat's Little Theorem, since 101 is prime and gcd(2,101)=1, 2^100 ≡ 1 (mod 101). Therefore 2^101 = 2 × 2^100 ≡ 2 × 1 = 2 (mod 101).
A.1
B.2✓ Correct
C.5
D.7
Explanation
By Fermat's Little Theorem, since 101 is prime and gcd(2,101)=1, 2^100 ≡ 1 (mod 101). Therefore 2^101 = 2 × 2^100 ≡ 2 × 1 = 2 (mod 101).
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