TITLE: For which integers x, y is $2^x + 3^y$ a square of a rational number?
QUESTION [7 upvotes]: For which integers x, y is $2^x + 3^y$ a square of a rational number?
(Of course $(x,y)=(0,1),(3,0)$ work)

REPLY [2 votes]: There are also negative integer solutions as well.  Consider $(-4,-2)$ where the expression then becomes $\frac{1}{16}+\frac{1}{9} = \frac{9}{144}+\frac{16}{144} = \frac{25}{144}$ which is the square of $\frac{5}{12}$.