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. odd number
• C. even number
• D. None of these

Answer 1

Answer: (A)

natural number greater than 1

Let $P\left(n\right):$ $n^p-n$

when $p=2$

$P\left(n\right)=$ $n^2-n$

$P\left(1\right)=0$ which is divisible all n$\in$N

$P\left(2\right)=2$ which is divisible by $2$

$P\left(3\right)=6$ which is divisible by $2$

Hence $P\left(n\right)$ is divisible by $2$ when $n$ is greater than $1$