The Diophantine Equation αm + βm + γm = 0

  • David Hilbert
Chapter

Abstract

Fermat advanced the conjecture that the equation
$${a^m} + {b^m} + {c^m} = 0$$
is not solvable in nonzero rational integers a, b, c if m > 2. Although there were already remarkable isolated results about this Fermat equation before the time of Kummer (Abel (1), Cauchy (1, 2). Dirichlet (1, 2, 3), Lamé (1, 2, 3), Lebesgue (1, 2, 3)) nevertheless Kummer, using the theory of ideals in regular cyclotomic fields, was the first to succeed in completely proving Fermat’s conjecture for a very extensive class of exponents m. The most important result obtained by Kummer is as follows.

Keywords

Fermat 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

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  • David Hilbert

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