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MathNet 2016-part-02 — 184 problems (EN–VI) Question 150

Math Olympiad Vault · MathNet 2016-part-02 — 184 problems (EN–VI)

Question 150

Find all triplets $(m, n, p)$ such that
$$
3^m p^2 + 1 = n^{2017},
$$
where $m$, $n$ are positive integers and $p$ is a prime number.