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Fermat’s little theorem – proofs that Fermat might have used

Published online by Cambridge University Press:  01 August 2016

R. P. Burn
R. P. Burn*
Affiliation:
Sunnyside, Barrack Road, Exeter EX2 6AB e-mail: [email protected]
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Extract

Fermat (1601-1665) is well-known for offering mathematical results without stating their proofs. In Mahoney’s fine mathematical biography, suggestions are made giving possible lines of reasoning which Fermat may have used, suggestions which are easily recognised by those familiar with number theory. This article offers some conjectured reconstructions of Fermat’s reasoning which may be more accessible to a beginner since they are linked to pattern recognition, and capitalise on the special cases with which Fermat illustrated his ideas. Generic examples played an essential part in Fermat’s exposition and may well have played a larger part in his proofs than would be respectable in a textbook nowadays.

Type
Articles
Information
The Mathematical Gazette , Volume 86 , Issue 507 , November 2002 , pp. 415 - 422
Copyright
Copyright © The Mathematical Association 2002

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References

1. Mahoney, M. S., The mathematical career of Pierre de Fermat, 1601–1665, (2nd edn), Princeton University Press (1994).Google Scholar
2. Fauvel, J. and Gray, J., The history of mathematics: a reader, Macmillan (1987).Google Scholar
3. Weil, A., Number theory, an approach through history; From Hammurapi to Legendre, Birkhäuser (1984).Google Scholar