If $$ x_i = 2^n + \sum_{j=0}^{n-1} x_j 2^j \;\; i \in {1,2}, $$
Is there an easy way that maybe I'm not aware of to find the number (just the number) of solutions such that
$$ x_1 x_2 =2^{2n+1}-2^{n-1} $$
?
I've tried to decompose the numbers $x_1,x_2$ using the binary representation, but It's too confusing to work out the solution, so I don't think that's the way.