Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon, the first step: the 641-gon

Helmut Ruhland

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arXiv · 2607.04000

Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon, the first step: the 641-gon

Helmut Ruhland

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Abstract

In an article, S. Adlaj showed the construction of the $F_4 = 65\,537$-gon ($F_4$ a Fermat prime). By extending the author's method to cases where the multiplicative group is not of order $2^n$ but has an additional prime factor, I here construct the $641$-gon. $641$ is the smaller prime factor of the composite Fermat number $F_5 = 2^{2^5} + 1$.

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Helmut Ruhland. 2026-07-04. Constructing the $\mathbf{2^{2^5} + 1 = F_5}$-gon, the first step: the 641-gon. https://arxiv.org/abs/2607.04000

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