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Pell's equation and Fermat

Published online by Cambridge University Press:  23 January 2015

Stan Dolan
Stan Dolan*
Affiliation:
126A Harpenden Road, St. Albans AL3 6BZ
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Extract

Given that it took until the 19th century for the case n = 5 of Fermat's last theorem to be settled, it is not surprising that Fermat's claim of having a proof for all exponents greater than 2 is nowadays treated with considerable scepticism. However, perhaps the most important aspect of his claim has been the impetus it has given to the development of mathematical techniques over the three and a half centuries leading up to the proof by Wiles and Taylor [1, 2]. Not least amongst these techniques has been Fermat's own idea of proof by descente infinie [3,4].

Type
Articles
Information
The Mathematical Gazette , Volume 96 , Issue 535 , March 2012 , pp. 66 - 70
Copyright
Copyright © The Mathematical Association 2012

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References

1. Wiles, A., Modular elliptic curves and Fermat's last theorem, Ann. of Math. (2) 141 (1995) pp. 443–551.CrossRefGoogle Scholar
2. Taylor, R. and Wiles, A., Ring theoretic properties of certain Heeke algebras, Ann. of Math. (2) 141 (1995) pp. 553–572.Google Scholar
3. Dolan, S., Fermat's method of ‘descente infinie’, Math. Gaz. 95 (July 2011) pp. 269–271.CrossRefGoogle Scholar
4. Dolan, S., Affirmative questions, Math. Gaz. 96 (Mar 2012) pp. 99–102.CrossRefGoogle Scholar
5. Heath, Sir T. L., Diophantus of Alexandria, Dover (1964).Google Scholar