For how many values of $a$ will the number $(a+1)(a-1)$ be prime?
I showed that $a$ must be even because if it is odd then $(a-1)(a+1)$ will be even and therefore not prime. If it is even, then I also showed that $a$ must be a multiple of $3$ because otherwise $(a-1)(a+1)$ will be a product of $3$. Seems like it's not the right method to find the number of $a$ that will give $(a+1)(a-1)$ prime?