# Too many pairs

Number Theory Level 4

Let's consider all the pairs of natural numbers ($$x$$;$$y$$) such that $$1\leq x\leq100$$, $$1\leq y\leq100$$ and $$x\neq y$$. Call $$S$$ the sum of all the products $$x*y$$. Which are the last 4 digits of $$S$$?

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