Geometry and Elementary Number Theory

Geometry Level 4

Let \(O\) be the origin. Given that the coordinates of the points \(A\) and \(B\) are \((0,n)\) and \((m,0)\) respectively, where \(m\) and \(n\) are integers. If the coordinates of the in-centre of \(\triangle OAB\) are \((3,3)\), then how many ordered pairs of integers \((m,n)\) are there?

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