Question 131
Let $n \geq 2$ be an integer. Consider the solutions $(a, b, c)$ of the system of equations
$$
\left\{\begin{array}{l}
n = a + b - c \\
n = a^{2} + b^{2} - c^{2}
\end{array}\right.
$$
where $a, b, c$ are integers. Prove that there is at least one solution and that there are finitely many solutions.
$$
\left\{\begin{array}{l}
n = a + b - c \\
n = a^{2} + b^{2} - c^{2}
\end{array}\right.
$$
where $a, b, c$ are integers. Prove that there is at least one solution and that there are finitely many solutions.