Question

What is the remainder when $2^{100}$ is divided by 101?

• A. 1
• B. 100
• C. 99
• D. None of these

Answer 1

The correct option is A 1

It is a direct application of Fermat’s Little theorem.
when p is a prime and a is a number co-prime to p ,then, a^(p-1) gives a remainder of 1 when divided by p.
101 is prime and 2 is co-prime to 101.
Hence, 2^100 will give a remainder of 1 when divided by 101.