Naslov
There are only finitely many Diophantine quintuples

Autori
Dujella, Andrej

Izvornik
Journal für die reine und angewandte Mathematik (0075-4102) 566 (2004), 1; 183-214

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Diophantine quintuples; Fermat

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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