If P is a prime number, then n p - n is divisible by p when n is a Options: A . &nbsp Natural number greater than 1 B . &nbsp Irrational number C . &nbsp Complex number D . &nbsp Odd number

If P is a prime number, then np - n is divisible by p when n is a

Question -

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

Options:

A . Natural number greater than 1

B . Irrational number

C . Complex number

D . Odd number

Answer: Option A
:
A

$n^{p}$ - 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.

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