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MathNet 2019-part-02 — 184 problems (EN–VI) Question 130

Math Olympiad Vault · MathNet 2019-part-02 — 184 problems (EN–VI)

Question 130

Find all pairs $(m, n)$ of positive integers for which there exists a prime number $p$ such that
$$
9^m + 3^m - 2 = 2p^n.
$$