Let $n$ be an integer. Prove that the integers $6n-1$, $6n+1$, $6n+2$, $6n+3$, and $6n+5$ are pairwise relatively prime.
I tried to prove that the first two integers in the list are relatively prime.
$$(6n-1-(6n+1)=1$$ $$6n-1-6n-1=1$$ $$-2=1,$$ which is obviously not true.
Not sure where to go from here. Is there another way to prove that two integers are relatively prime?