Question 86
Determine all positive integers $n$, with $n \ge 2$, such that the equation
$$
x^2 - 3 \cdot x + 5 = 0 \quad (1)
$$
has a unique solution in the ring $(\mathbb{Z}_n, +, \cdot)$.
$$
x^2 - 3 \cdot x + 5 = 0 \quad (1)
$$
has a unique solution in the ring $(\mathbb{Z}_n, +, \cdot)$.