Question 105
Let $n \in \mathbb{N}$, $n \ge 4$ and $a_1, a_2, \dots, a_n$ be real numbers such that
$$
a_k^3 = a_{k+1}^2 + a_{k+2}^2 + a_{k+3}^2
$$
for all $k \in \{1, 2, \dots, n\}$ – indices are considered modulo $n$. Show that $a_1 = a_2 = \dots = a_n$.
$$
a_k^3 = a_{k+1}^2 + a_{k+2}^2 + a_{k+3}^2
$$
for all $k \in \{1, 2, \dots, n\}$ – indices are considered modulo $n$. Show that $a_1 = a_2 = \dots = a_n$.