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Omni-MATH / Find the unique pair of positive integers (a,b) with a<b for which (2020−a)/(a)⋅(2020−b)/(b)=2

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problem

Find the unique pair of positive integers (a,b)(a, b) with a<ba<b for which 2020−aa⋅2020−bb=2\frac{2020-a}{a} \cdot \frac{2020-b}{b}=2
Plain-text mathematical notation (without MathML)
Find the unique pair of positive integers (a,b) with a<b for which (2020−a)/(a)⋅(2020−b)/(b)=2
Original LaTeX notation
Find the unique pair of positive integers $(a, b)$ with $a<b$ for which $$\frac{2020-a}{a} \cdot \frac{2020-b}{b}=2$$

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