Competition problem — Number theory

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Number theory Difficulty 5.3 AIME, harder Find the answer

13. Estimate the number of decimal digits in the Fermat number $F_{n}$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

13. $2^{n} \log _{10} 2$

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.