Question 131
For any non-zero natural number $n$ consider the set
$$
A = \{n^2, n^2 + 1, n^2 + 2, \dots, (n+1)^2\}.
$$
Find the numbers $a, b, c \in A$, $a \lt b \lt c$, knowing that $b$ is the geometric mean of the numbers $a$ and $c$.
$$
A = \{n^2, n^2 + 1, n^2 + 2, \dots, (n+1)^2\}.
$$
Find the numbers $a, b, c \in A$, $a \lt b \lt c$, knowing that $b$ is the geometric mean of the numbers $a$ and $c$.