How many ordered pairs of positive integers (x,y) satisfy the equation x=4-x over y^2-x?
x = (4 - x) / ( y^2 - x) rearrange as
y^2 - x = (4 - x) / x
y^2 = 4/x - 1 + x
y^2 = ( x - 1) + 4/x
Note that ( x - 1) will be an integer for all integer values for x
But 4/x will only be an integer when x = 1, 2 or 4
When x = 1, y = 2
When x = 2, y = √3
When x = 4, y = 2
However....(4,2) produces a denominator = 0 in the original equation....so....this answer must be rejected...!!!
So.....(1,2) is the only correct answer
EDIT : Thanks to hectictar for spotting my preious error !!!!