Question 119
Let
$$
S_n = \{x^2 + n y^2 : x, y \in \mathbb{Z}\}.
$$
Find all positive integers $n$ such that there exists an element of $S_n$ which doesn't belong to any of the sets $S_1, S_2, \dots, S_{n-1}$.
$$
S_n = \{x^2 + n y^2 : x, y \in \mathbb{Z}\}.
$$
Find all positive integers $n$ such that there exists an element of $S_n$ which doesn't belong to any of the sets $S_1, S_2, \dots, S_{n-1}$.