Competition problem — Number theory

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Number theory Difficulty 5.8 AIME, harder Prove it

7. Use Pepin's test to show that the following Fermat numbers are primes
a) $\quad F_{1}=5$
b) $\quad F_{3}=257$
c) $\quad F_{4}=65537$ .

Solution

None

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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.