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\[ \left \lfloor \frac { { a }^{ 2 } }{ { b }^{ 2 } } \right \rfloor +\left \lfloor \frac { { b }^{ 2 } }{ { a }^{ 2 } } \right \rfloor = \left \lfloor \frac { { a }^{ 2 }+{ b }^{ 2 } }{ ab } \right \rfloor + ab\]

If there exists a least pair of natural numbers \((x, y)\) to the equation above for positive natural \(a\) and \(b\), find \(x + y\).

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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