Using the Fermat–Euler theorem, argue that (i) Fermat’s Little Theorem holds. (ii) a−1in Zn is aϕ(n)−1 mod n, for any a ∈ Zn that is relatively prime to n. Verify the latter claim for the...

Using the Fermat–Euler theorem, argue that

(i) Fermat’s Little Theorem holds.

(ii) a−1in Zn is aϕ(n)−1 mod n, for any a ∈ Zn that is relatively prime to n.

Verify the latter claim for the multiplicative inverses of a ∈ {7, 17, 31} in Z60