Find the greatest common divisor (gcd) of $n^2 - 3n - 1$ and $2$ Find the greatest common divisor (gcd) of $n^2 - 3n - 1$ and $2$ considering that $n$ is an integer. Thanks.

Hint $\ $ One of $\,\ n,\,\ n\!-\!3\,$ is even so $\ n(n\!-\!3)-1\,$ is odd, so coprime to $\,2.$
Alternatively $\,2\nmid f(n)=n^2-3n-1\,$ since $f$ has no roots mod $\,2\!:\ f(0)\equiv 1\equiv f(1),\,$ which is a special case of the Parity Root Test.
