Question

If p is a prime number, then $n^p-n$ is divisible by p when n is a

• A. Natural number greater than 1
• B. Irrational number
• C. Complex number
• D. Odd number

Answer 1

The correct option is A Natural number greater than 1

$n^p-n$ is divisible by p for any natural number greater than 1. It is Fermet’s theorem.
Trick : Let n = 4 and p = 2
Then $(4{)}^2-4=16-4=12$ , it is divisible by 2. So, it is true for any natural number greater than 1.