Is there infinite number of postive integer pairs $(p>q)$ ,such $3(2^p+1)=(2^q+1)^2$ Is there infinite number of  postive integer pairs $(p>q)$
$$3(2^p+1)=(2^q+1)^2$$
I add my some approach 
$$3\cdot 2^p+3=4^q+2^{q+1}+1$$
Give by
$$2^{2q-1}+2^q=3\cdot 2^{p-1}+1$$ I don't see how to proceed from this point

Look at the binary digits of both sides.
Or consider the remainders $\bmod 4$
