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MathNet 2023-part-06 — 191 problems (EN–VI) Question 150

Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)

Question 150

Find all triples $(n, k, p)$ satisfying the equation
$$
|6n^2 - 17n - 39| = p^k
$$
where $n, k$ are integers and $p$ is a prime.