TR-MO-R1 2022 Problem 30

$m$ ve $n$ pozitif tam sayılar ve $p$ bir asal sayı olmak üzere, $2m^2+3m-44 = 3p^n$ eşitliğini sağlayan kaç $(m, n, p)$ üçlüsü vardır?

a) $1$ b) $2$ c) $3$ d) $4$ e) $5$

Official text Turkish Mathematical Olympiad, first round 2022 official paper, page 17. Quoted with source.

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