Consider the following statements : S n > 1, aϕ(n) ≡ 1(mod n)

1 : For any integer a ∈ Z∗ ϕ(n) for all n , where is Euler's phi function. S p ap ≡ 1(mod p)

2 : If is prime, then for all a ∈ Z∗ p . Which one of the following is/are correct? S

1. AOnly 1 S
2. BOnly 2 S S
3. CBoth 1 and 2 S S
4. DNeither 1 nor 2

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. Only 1 S

Explanation

Euler's theorem gives a^φ(n) ≡ 1 (mod n) for a coprime to n (S1 true). Fermat says a^(p−1) ≡ 1 (mod p), not aᵖ ≡ 1 (S2 false).