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Print59th Ukrainian National Mathematical Olympiad
Ukraine algebra
Problem
Determine if there exists a pair of proper fractions that cannot be simplified so that their difference equals their product and one of denominators is . If such pair exists, find at least two of such pairs of fractions.
Solution
The solution is based on a simple fact: .
Final answer
(1/2019, 1/2020) and (1/2018, 1/2019)
Techniques
Fractions