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MathNet 2019-part-07 — 184 problems (EN–VI) Question 91

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

Question 91

Find all natural numbers $a$ and $b$, for which the number $2^{a!} + 2^{b!}$ is a cube of a natural number.
*Recall that for a natural number $n$, $n! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot n$.*

(Arseniy Nicolaev)