Explanation:

Let p = 5
Then Np−1 − 1
= N⁵⁻¹ − 1
= N^{4 − 1} ………. (i)
As, N is prime to p
So Let N = 3
Then from (i)
N⁴ − 1 = 3⁴ − 1 = 81 − 1 = 80
Here, (N^p−1 − 1) is a multiple of p .Here, given condition had satisfied when p is a prime number.