Trustworthy Systems

A string of pearls: Proofs of fermat's little theorem


Joseph Chan and Michael Norrish

Australian National University



We discuss mechanised proofs of Fermat’s Little Theorem in a variety of styles, focusing in particular on an elegant combinatorial “necklace” proof that has not been mechanised previously. What is elegant in prose turns out to be long-winded mechanically, and so we examine the effect of explicitly appealing to group theory. This has pleasant consequences both for the necklace proof, and also for some of the direct number-theoretic approaches.

BibTeX Entry

    author           = {Chan, Joseph and Norrish, Michael},
    journal          = {Journal of Formal Reasoning},
    keywords         = {mechanised mathematics},
    month            = dec,
    number           = {1},
    pages            = {63--87},
    paperurl         = {},
    title            = {A string of pearls: proofs of Fermat's Little Theorem},
    volume           = {6},
    year             = {2013}