Speculation of Fermat’s proof of his Last Theorem

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 5, 1999, Number 2, Pages 71—79
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Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006, Australia

A. G. Shannon
University of Technology, Sydney, 2007, Australia

Abstract

It has been suspected that if Fermat did indeed have a simple proof for his famous ‘last theorem’, that he probably employed his method of infinite descent. In a renewed attempt to see how Fermat might have thought that he had proved that if cn = an + bn, a, b, c, n ∈ ℤ, n > 2, then a, b, c cannot all be integers, we set c = a + b + m, m ∈ ℤ, and then raised it to the n-th power. The roots of the resulting polynomial in m appear to be — (a + b) only when n ≠ 1 ,2 , and the result might have seemed to Fermat to follow from this. The plausibility of the algebra developed here is considered in the context of the work of the sixteenth century mathematicians, particularly Cardano and Bombelli.

AMS Classification

  • 01A45
  • 11D41

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Cite this paper

Leyendekkers, J. V. & Shannon, A. G. (1999). Speculation of Fermat’s proof of his Last Theorem. Notes on Number Theory and Discrete Mathematics, 5(2), 71-79.

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