The Diophantine Equation α m + β m + γ m = 0

David Hilbert

Chapter 36 in The Theory of Algebraic Number Fields, 1998, pp 327-333 from Springer

Abstract: 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: Class Number; Semi Primary; Diophantine Equation; Quadratic Field; Extensive Class (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-3-662-03545-0_36

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