2017 · Q48
(Nᵖ⁻¹-1) is a multiple of p, if N is prime to p and p is a
Elementary MathematicsNumber System
- APrime number
- BRational number
- CReal number
- DComposite number
Explanation
This is Fermat's little theorem: if p is prime and N is coprime to p, then N^(p-1) ≡ 1 (mod p), i.e. p divides N^(p-1) - 1. The primality of p is essential — for composite p the statement fails in general (e.g. N = 2, p = 4: 2³ - 1 = 7 is not a multiple of 4). Hence p must be a prime number. Option (a).