Number Theory Problem by Ashu Dablo

\(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{580909190400000}\) has \(n\) ordered pairs of positive integral solutions .

Find \(n\) \(\mod (2\times3\times5\times7)\)

Note: This problem can be solved with a little patience and pencil and paper and so, please refrain from using computational aids.

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