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MathNet 2015-part-03 — 191 problems (EN–VI) Question 158

Math Olympiad Vault · MathNet 2015-part-03 — 191 problems (EN–VI)

Question 158

Does there exist positive integers $a$, $b$ and a prime $p$ such that
$$
a^{3}-b^{3}=4 p^{2} ?
$$