Fermat-Like Binomial Equations

Heiko Harborth

A chapter in Applications of Fibonacci Numbers, 1988, pp 1-5 from Springer

Abstract: Abstract For more than three centuries it has been a conjecture that the Diophantine equation (1) $$ {x^n} + {y^{_n}} = {z^n} $$ has no solutions in natural numbers x, y, z for all n > 2. At present this conjecture, which is also called ”Fermat’s Last Theorem”, is known to be true for all n ≤ 125 000 [1]. Moreover, the recent work of G. Faltings (see [1]) implies that, for each n ≥ 3, (1) has at most a finite number of solutions (x, y, z), with (x, y, z) = 1 and xyz ≠ 0.

Keywords: Recent Work; Natural Number; Finite Number; Diophantine Equation; Elementary Theory (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-7801-1_1

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DOI: 10.1007/978-94-015-7801-1_1

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