Naslov
On the number of D(4)-quintuples

Autori
Baćić, Ljubica ; Filipin, Alan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
29th Journées Arithmétiques / - Deberecen, 2015, 28-29

Skup
29th Journées Arithmétiques

Mjesto i datum
Debrecen, Mađarska, 06.07.2015. - 10.07.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine m-tuples; quintuple

Sažetak
We call the set of m positive distinct integers a D(4)-m-tuple if the prod- uct of any of its two elements increased by 4 is a perfect square. The folklore conjecture states that there exists no D(4)-quintuple. In this talk we will present how to improve the known bound on the number of D(4)-quintuples, illustrating the more efficient way of counting the number of m-tuples using divisor sums. More precisely, we prove that there are at most 7*10^36 D(4)-quintuples.

Izvorni jezik
Engleski

POVEZANOST RADA