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MathNet 2025-part-02 — 186 problems (EN–VI) Question 89

Math Olympiad Vault · MathNet 2025-part-02 — 186 problems (EN–VI)

Question 89

Find all positive integers $n$ that cannot be written in the form
$$
n = \frac{a}{b} + \frac{a+1}{b+1},
$$
where $a$ and $b$ are positive integers.