Muhammad's least list

How many ordered pairs of positive integers (x,y)(x,y) satisfy

lcm(x,y)=10004000600040001? \text{lcm} (x, y) = 10004000600040001 ?

This problem is shared by Muhammad A.

Details and assumptions

lcm(x,y)(x,y) denotes the least common multiple of x x and yy.

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