Naslov
An absolute bound for the size of Diophantine m-tuples

Autori
Dujella, Andrej

Izvornik
Journal of Number Theory (0022-314X) 89 (2001), 1; 126-150

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

Ključne riječi
Diophantine m-tuples; simultaneous Pellian equations; common terms in recurrence sequences; linear form in logarithms

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. We prove that if {a,b,c} is a Diophantine triple such that b > 4a and c > max {b^{13}, 10^{20}} or c > max {b^{5}, 10^{1029}}, then there is unique positive integer d such that d > c and {a,b,c,d} is a Diophantine quadruple. Furthermore, we prove that there does not exist a Diophantine 9-tuple and that there are only finitely many Diophantine 8-tuples.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA