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MathNet 2017-part-02 — 176 problems (EN–VI) Question 47

Math Olympiad Vault · MathNet 2017-part-02 — 176 problems (EN–VI)

Question 47

Find all positive integers $n$ for which there exist positive integers $a$ and $b$ such that
$$
(n^2 + 2)^a = (2n - 1)^b.
$$