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MathNet 2022-part-06 — 196 problems (EN–VI) Question 62

Math Olympiad Vault · MathNet 2022-part-06 — 196 problems (EN–VI)

Question 62

Is
$$
\prod_{k=0}^{\infty}\left(1-\frac{1}{2022^{k!}}\right)
$$
rational?