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Nonexistence of D(4)-quintuples (CROSBI ID 651740)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Filipin, Alan ; Bliznac Trebješanin, Marija Nonexistence of D(4)-quintuples // 19TH ÖMG CONGRESS AND ANNUAL DMV MEETING. 2017. str. 93-93

Podaci o odgovornosti

Filipin, Alan ; Bliznac Trebješanin, Marija

engleski

Nonexistence of D(4)-quintuples

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.

Diophantine m-tuples

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o prilogu

93-93.

2017.

objavljeno

Podaci o matičnoj publikaciji

19TH ÖMG CONGRESS AND ANNUAL DMV MEETING

Podaci o skupu

19TH ÖMG CONGRESS AND ANNUAL DMV MEETING

predavanje

11.09.2017-15.09.2017

Salzburg, Austrija

Povezanost rada

Matematika