Construction of Regular Prime p-Gon Exists iff p is Fermat Prime/Historical Note

Historical Note on Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime
The result Construction of Regular Prime $p$-Gon Exists iff $p$ is Fermat Prime was stated, but not proved, by, who demonstrated the result for $n = 17$ in $1796$.

The case $p = 257$ was demonstrated by in $1832$.

The case $p = 65 \, 537$ was attempted by, who offered a construction in $1894$ after a decade of work. However, it has been suggested that there are mistakes in his work.

The cases where $p = 3$ and $p = 5$ were known to the ancient Greeks and are given in.