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Question

What is the remainder when 2100 is divided by 101?
  1. 1
  2. 99
  3. None of these
  4. 100


Solution

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.

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