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CONO-SUR 2010 Problem 1

    Pedro must choose two irreducible fractions, each with a positive numerator and denominator such that:

    • The sum of the fractions is equal to 22 .
    • The sum of the numerators of the fractions is equal to 10001000 .

    In how many ways can Pedro do this?

    Dataset text AI-MO AoPS. Quoted with source.

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