Question 73
Let $n$ be a fixed positive integer. Find all triples $(a, b, c)$ of integers satisfying the following system of equations:
$$
\begin{cases}
a^{n+3} + b^{n+2}c + c^{n+1}a^2 + a^n b^3 = 0 \\
b^{n+3} + c^{n+2}a + a^{n+1}b^2 + b^n c^3 = 0 \\
c^{n+3} + a^{n+2}b + b^{n+1}c^2 + c^n a^3 = 0
\end{cases}
$$
$$
\begin{cases}
a^{n+3} + b^{n+2}c + c^{n+1}a^2 + a^n b^3 = 0 \\
b^{n+3} + c^{n+2}a + a^{n+1}b^2 + b^n c^3 = 0 \\
c^{n+3} + a^{n+2}b + b^{n+1}c^2 + c^n a^3 = 0
\end{cases}
$$