Question 117
Determine all pairs $(m, p)$ of natural numbers such that $p$ is a prime number and
$$
2^{m} p^{2}+27
$$
is the third power of a natural number.
$$
2^{m} p^{2}+27
$$
is the third power of a natural number.
MathNet 2015-part-06 — 191 problems (EN–VI) Question 117
Math Olympiad Vault · MathNet 2015-part-06 — 191 problems (EN–VI)