MathDB

Denote a set of equations in the real numbers with variables

x_1, x_2, x_3 \in \mathbb{R}

Flensburgian if there exists an

i \in \{1, 2, 3\}

such that every solution of the set of equations where all the variables are pairwise different, satisfies

x_i>x_j

for all

j \neq i

.
Find all positive integers

n \geq 2

, such that the following set of two equations

a^n+b=a

and

c^{n+1}+b^2=ab

in three real variables

a,b,c

is Flensburgian.

Problem Statement