Question 1
Determine, with proof, whether there is any odd integer $n \ge 3$ and $n$ distinct prime numbers $p_1, p_2, \dots, p_n$ such that all $p_i + p_{i+1}$ ($i = 1, 2, \dots, n$, and $p_{n+1} = p_1$) are perfect squares? (posed by Tao Pingsheng)