Question

If 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.