On the inverse Fermat equation
type: Item
instance of: scholarly article
title: On the inverse Fermat equation
zbMATH Open document ID: 0766.11018
DOI: 10.1016/0012-365X(92)90561-S
published in: Discrete Mathematics
publication date: 1993-01-16T00:00:00Z
review text: The inverse Fermat equation \(x^{1/n}+ y^{1/n}=z^{1/n}\) is solved in positive integers \(x\), \(y\), \(z\), \(n\). If the \(n\)th roots are taken to be positive real numbers, it is equivalent to the following problem: if \(\alpha\), \(\beta\) are positive real numbers for which \(\alpha+\beta=1\), \(\alpha^ n\) and \(\beta^ n\) are rational, then \(\alpha\) and \(\beta\) are rational. The proof is very short called a ``one line proof''. If the \(n\)th roots rather than positive real ones are allowed in the equation, the author proves that up to a suitable equivalence relation there are exactly four nontrivial solutions.
reviewed by: Xu Guangshan
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 94538
zbMATH Keywords: inverse Fermat equation
Wikidata QID: Q56002641
author: H. W. jun. Lenstra
MaRDI profile type: Publication
cites work: A radical diophantine equation
cites work: Q3029073
full work available at URL: 0012-365x(92)90561-s
OpenAlex ID: W1996140314
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description: scientific article; zbMATH DE number 94538