JEE maths#18

Algebra Level 4

S=121×3+223×5+325×7++5002999×1001\large S = \frac{1^{2}}{1\times3} + \frac{2^{2}}{3\times5} + \frac{3^{2}}{5\times7} + \cdots + \frac{500^{2}}{999\times1001}

For SS as defined above, find the number of divisors of S \left \lfloor S \right \rfloor.


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


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