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diophantine with prime p, 2^mp^2 + 27 = q^3 (HOMC 2017 J Q6)

Source:

August 7, 2019
number theoryDiophantine equationprimediophantine

Problem Statement

Find all triples of positive integers (m,p,q)(m,p,q) such that 2mp2+27=q32^mp^2 + 27 = q^3 and pp is a prime.
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