Assume that x >= 3, then:
x^4 > x^3 + x^3 + x + x
x^4 > x^2*y +x*y^2 + x + y
x^4 + y^4 > x^2*y +x*y^2 + x + y
This contradicts the given equation, therefore 3 > x.

The potential solutions are then limited to (0,0),(1,0),(2,0)(1,1),(2,1), and (2,2).
Of these possibilites only (0,0) and (1,0) are solutions.

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