For an arbitrary integer $n$, let $g(n)$ be the GCD of $2n + 9$ and $6n^2 + 11n - 2$. What is the largest positive integer that can be obtained as the value of $g(n)$? If $g(n)$ can be arbitrarily large, state so explicitly and prove it.
For an arbitrary integer $n$, let $g(n)$ be the GCD of $2n + 9$ and $6n^2 + 11n - 2$. What is the largest positive integer that can be obtained as the value of $g(n)$? If $g(n)$ can be arbitrarily large, state so explicitly and prove it.