How many ordered pairs of integers (x, y) satisfy the equation x2 + xy + y2 = x2y2

To solve this problem, we need to find the ordered pairs of integers (x, y) that satisfy the equation x^2 + xy + y^2 = x^2y^2.

Step 1: Rewrite the equation to make it easier to solve.

x^2 + xy + y^2 - x^2y^2 = 0

Step 2: Factor the equation.

x^2(1 - y^2) + xy + y^2 = 0

Step 3: Set each factor equal to zero and solve for x and y.

x^2(1 - y^2) = 0 --> x = 0 or y = ±1

xy = 0 --> x = 0 or y = 0

y^2 = 0 --> y = 0

Step 4: Find the ordered pairs (x, y) that satisfy these solutions.

The solutions are (0, 0), (0, 1), (0, -1), (1, 0), and (-1, 0).

So, there are 5 ordered pairs of integers (x, y) that satisfy the equation x^2 + xy + y^2 = x^2y^2.