Number Theory Problem by Ashu Dablo

1x+1y=1580909190400000\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{580909190400000} has nn ordered pairs of positive integral solutions .

Find nn mod(2×3×5×7)\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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