Solve (pen and paper only):

**5*3**^{x}+4=y^{2}

List all possible integer solutions.

a few very small steps:

clearly x is not negative else the LHS is not integer.

x = 0 and y= +/- 3 is a solution.

for all y that work, so does -y, as LHS is positive

x are even, since this produces LHS numbers ending in ..09 and ...49

(x odd makes numbers ending in 19 and 39 which can not be squares)

likewise y ends in 3 or 7

I wonder how 5*3^x=(y-2)(y+2) might help

*Edited on ***June 25, 2018, 6:19 am**

*Edited on ***June 25, 2018, 7:38 am**