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

Authors:
Hing-Lun Chan;Michael Norrish
Affiliations:
Australian National University, Australia;Canberra Research Lab, NICTA, Australia,Australian National University, Australia
Venue:
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
Year:
2012

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Abstract

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 the direct number-theoretic approach.