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There are only finitely many Diophantine quintuples (CROSBI ID 104864)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej There are only finitely many Diophantine quintuples // Journal für die Reine und Angewandte Mathematik, 566 (2004), 1; 183-214-x

Podaci o odgovornosti

Dujella, Andrej

engleski

There are only finitely many Diophantine quintuples

A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct elements increased by 1 is a perfect square. Diophantus found a set of four positive rationals with the above property. The first Diophantine quadruple was found by Fermat (the set {; ; 1, 3, 8, 120}; ; ). Baker and Davenport proved that this particular quadruple cannot be extended to a Diophantine quintuple. In this paper, we prove that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples.

Diophantine quintuples; Fermat

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Podaci o izdanju

566 (1)

2004.

183-214-x

objavljeno

0075-4102

Povezanost rada

Matematika

Indeksiranost