Find G. C. F. of $(8n^3 + 8n, 2n+1)$ I'm stuck with this problem, I divided $8n^3 + 8n$ by $2n+1$ and obtained $5$, so now my G. C. F is $\gcd(2n+1, -5)$.
What's next? I can't divide $2n+1$ by $-5$.

Since $8n^3+8n=(2n+1)[4n^2-2n+5]-5$, we have that $\gcd(8n^3+8n,2n+1)$ divides $5$ and so is either $1$ or $5$. Both cases do occur:
For $n=1$, we get $\gcd(8n^3+8n,2n+1)=1$.
For $n=2$, we get $\gcd(8n^3+8n,2n+1)=5$.
In fact, 
$\gcd(8n^3+8n,2n+1)=5$ iff $n \equiv 2 \bmod 5$; otherwise $\gcd(8n^3+8n,2n+1)=1$.
