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Sum of two fractions

Source: Cono Sur 2010 #1

November 17, 2015
number theorycono sur

Problem Statement

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?
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