Naslov
Nonexistence of D(4)-quintuples

Autori
Filipin, Alan ; Bliznac Trebješanin, Marija

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

Izvornik
19TH ÖMG CONGRESS AND ANNUAL DMV MEETING / - , 2017, 93-93

Skup
19TH ÖMG CONGRESS AND ANNUAL DMV MEETING

Mjesto i datum
Salzburg, Austrija, 11.09.2017. - 15.09.2017

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Diophantine m-tuples

Sažetak
Let n be a nonzero integer. A set of m distinct positive integers such that the product of any two of its elements increased by n is a perfect square is called D(n)-m-tuple. One of the question of interest is how large those sets can be. The most studied case is n = 1, and very recently He, Togbé and Ziegler announced the proof of the folklore conjecture, that there does not exist a D(1)-quintuple. In this talk we will consider the case n = 4. There is also a conjecture that there does not exist a D(4)-quintuple. The cases n = 1 and n = 4 are closely connected and usually the same methods work. However, D(4) case is sometimes technically more challenging. We will give the proof of nonexistence of D(4)-quintuples, focusing on parts that are different from D(1) case.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA