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MathNet 2019-part-07 — 184 problems (EN–VI) Question 95

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 95

Find all natural numbers $a$, $b$ and $c$, such that the number $2^{a!} + 2^{b!} + 2^{c!}$ is a cube of a natural number.
(Arseniy Nicolaev)