Competition problem — Number theory

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Number theory Difficulty 6.2 National olympiad Prove it

Example 1
Define "Fermat number": $F_{n}=2^{2 n}+1$ . When $n>1$ , prove: if prime $p$ is a factor of $F_{n}$ , then $p \equiv 1\left(\bmod 2^{n+1}\right)$

Solution

None

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None

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