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XXVII.—On Fermat's Theorem

Published online by Cambridge University Press:  17 January 2013

H. F. Talbot Esq.
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Extract

It is well known that no satisfactory demonstration has ever been given of Fermat's celebrated theorem, which asserts that the equation an = bn + cn is impossible, if a, b, c, are whole numbers, and n is any whole number greater than 2. In Legendre's Théorie des Nombres, he demonstrates the cases of n = 3, n = 4, and n = 5, the latter only in his Second Supplement. In Crelle's Mathematical Journal, ix. 390, M. Dirichlet, a mathematician of Berlin, has demonstrated the case of n = 14, but I am not aware whether his demonstration is considered successful. Legendre informs us (Second Supplement, p. 3) that the Academy of Sciences, with the view of doing honour to the memory of Fermat, proposed, as the subject of one of its mathematical prizes, the demonstration of this theorem; but the Concourse, though prolonged beyond the usual term, produced no result.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 21 , Issue 3 , 1857 , pp. 403 - 406
Copyright
Copyright © Royal Society of Edinburgh 1857

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References

page 403 note * “Cubum autem in duos cubos aut quadrato-quadratum in duos quadrato-quadratos et generaliter nullam in infinitum, ultra quadratum, potestatem in duos ejusdem nominis fas est dividere. Cujus rei demonstrationem mirabilem sanè detexi. Hanc marginis exiguitas non caperet.”—Fermat, Notes sur Diophante, p. 61.