Ordered pairs of a, b

Find all ordered pairs (a,b) of positive integers for which \frac{1}{a}+\frac{1}{b}=\frac{3}{2018}.

Source: Putnam

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The six ordered pairs are (1009, 2018),(2018, 1009),(1009 · 337, 674) = (350143, 674),(1009 · 1346, 673) = (1358114, 673),(674, 1009 · 337) = (674, 350143),
and (673, 1009 · 1346) = (673, 1358114).

Video solution

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Putnam Exam | 2018: A1 - YouTube