The Diophantine Equation αm + βm + γm = 0

  • David Hilbert


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.


Class Number Semi Primary Diophantine Equation Quadratic Field Extensive Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • David Hilbert

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