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MathNet 2007-part-02 — 187 problems (EN–VI) Question 154

Math Olympiad Vault · MathNet 2007-part-02 — 187 problems (EN–VI)

Question 154

How many ordered pairs $(x, y)$ of positive integers, where $x \lt y$, satisfy the equation
$$
\frac{1}{x} + \frac{1}{y} = \frac{1}{2007}
$$