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Question 52

For any natural number k , let $$a_{k}=3^{k}$$. The smallest natural number m for which $$\left\{(a_{1})^{1}\times(a_{2})^{2}\times...\times(a_{20})^{20}\right\}<\left\{a_{21}\times a_{22}\times...\times a_{20+m}\right\}$$, is

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