Windmills of the Minds: An Algorithm for Fermat's Two Squares Theorem

Hing Lun Chan*

*Corresponding author for this work

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    2 Citations (Scopus)

    Abstract

    The two squares theorem of Fermat is a gem in number theory, with a spectacular one-sentence "proof from the Book". Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves involutions on a finite set, especially the parity of the number of fixed points in the involutions. Starting as an existence proof that is non-constructive, there is an ingenious way to turn it into a constructive one. This gives an algorithm to compute the two squares by iterating the two involutions alternatively from a known fixed point.

    Original languageEnglish
    Title of host publicationCPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022
    EditorsAndrei Popescu, Steve Zdancewic
    PublisherAssociation for Computing Machinery, Inc
    Pages251-264
    Number of pages14
    ISBN (Electronic)9781450391825
    DOIs
    Publication statusPublished - 17 Jan 2022
    Event11th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2022 - co-located with POPL 2022 - Philadelphia, United States
    Duration: 17 Jan 202218 Jan 2022

    Publication series

    NameCPP 2022 - Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs, co-located with POPL 2022

    Conference

    Conference11th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2022 - co-located with POPL 2022
    Country/TerritoryUnited States
    CityPhiladelphia
    Period17/01/2218/01/22

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