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PreprintCC BY-NC-ND 4.0arXiv

Constructing the 225 + 1 = F5-gon, the first step: the 641-gon

  • Helmut Ruhland
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Abstract

In an article, S. Adlaj showed the construction of the F4 = 65 537-gon (F4 a Fermat prime). By extending the author's method to cases where the multiplicative group is not of order 2n but has an additional prime factor, I here construct the $641$-gon. $641$ is the smaller prime factor of the composite Fermat number F5 = 225 + 1.

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Cite

BibTeXRIS
BibTeX
@misc{ruhland2026constructing,
  title = {{Constructing the $\mathbf2^2^5 + 1 = F_5$-gon, the first step: the 641-gon}},
  author = {Helmut Ruhland},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.04000},
  eprint = {2607.04000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.04000},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Constructing the 2^2^5 + 1 = F_5-gon, the first step: the 641-gon
AU  - Helmut Ruhland
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2607.04000
UR  - https://arxiv.org/abs/2607.04000
AB  - 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.
ER  -