Divisor of Fermat Number/Historical Note

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Historical Note on Divisor of Fermat Number

In $1747$, Leonhard Paul Euler proved that a divisor of a Fermat number $F_n$ is always in the form $k \, 2^{n + 1} + 1$.

This was later refined to $k \, 2^{n + 2} + 1$ by François Édouard Anatole Lucas.