# A Number Theory Problem by Muhammad Rasel Parvej

$\dfrac{1}{1-2^{2}}+\dfrac{1}{1-4^{2}}+\dfrac{1}{1-6^{2}}+\dfrac{1}{1-8^{2}}+\cdots+\dfrac{1}{1-1000^{2}}\$

The value of the expression above can be expressed as $$\dfrac{a}{b},$$ where $$a$$ and $$b$$ are coprime integers.

What is the number of ways (equivalently, the number of ordered pair of integers $$(a,b)$$ ) the value of the expression above can be expressed as $$\dfrac{a}{b},$$ where $$a$$ and $$b$$ are coprime integers.

Hint: Is it at all needed to compute the sum?

×