if log(base2(5x+3y)) + log(base2(5x-3y)) = 10 where x and y are integers, the no of possible values of (x,y) is??? ans = 4.. approach plz

Hi Manini,
The solution to this question goes like this:
log(base2(5x+3y)) + log(base2(5x-3y)) = 10
(5x+3y)(5x-3y) = 2^{10} = 1024
Suppose 5x+3y = 1 and 5x-3y = 1024 or vice versa
This does not provide an integral value of x.
Suppose 5x+3y = 2 and 5x-3y = 512 or vice versa
This does not provide an integral value of x.
Suppose 5x+3y = 4 and 5x-3y = 256 or vice versa
This provides an integral value of x.
Similarly the other solution would be 5x+3y = 16 and 5x-3y = 64 or vice versa which would give integral value of x.