Divisor of Fermat Number/Historical Note

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.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $257$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$