Question 187
a. Solve the equation $x^{2}-x+\hat{2}=\hat{0}$, $x \in \mathbb{Z}_{7}$.
b. Determine the natural numbers $n \ge 2$ for which the equation $x^{2}-x+\hat{2}=\hat{0}$ has a unique solution $x \in \mathbb{Z}_{n}$.
b. Determine the natural numbers $n \ge 2$ for which the equation $x^{2}-x+\hat{2}=\hat{0}$ has a unique solution $x \in \mathbb{Z}_{n}$.