Question 74
Denote a set of equations in the real numbers with variables $x_1, \dots, x_m \in \mathbb{R}$ Flensburgian if there exists an $i \in \{1, \dots, m\}$ such that every solution of the set of equations where all the variables are pairwise different, satisfies $x_i \gt x_j$ for all $j \ne i$.
Determine for which positive integer $n \ge 1$, the following set of two equations
$$
a^n + b = a \text{ and } c^{n+1} + b^2 = ab
$$
in the three real variables $a, b, c$ is Flensburgian.
Determine for which positive integer $n \ge 1$, the following set of two equations
$$
a^n + b = a \text{ and } c^{n+1} + b^2 = ab
$$
in the three real variables $a, b, c$ is Flensburgian.