Naslov
Upper bound on number of D(4)-quintuples

Autori
Bliznac, Marija ; Filipin, Alan

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Izvornik
6th Croatian Mathematical Congress / - , 2016

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Poster

Vrsta recenzije
Nije recenziran

Ključne riječi
Diophnatine m-tuples
(Diophantine m-tuples)

Sažetak
We call the set of m positive distinct integers D(n)-m-tuple if the product of any of its two elements increased by n is a perfect square. It is conjectured that there does not exist a D(4)-quintuple and we will present some results that support that conjecture. We will show how we improved previous results on the upper bound of D(4)-quintuples, more precisely, we prove there is at most 6.8587⋅10^29 D(4)-quintuples. In the proof we use the standard methods used in solving similar problems, solving the system of simultaneous Pellian equations, and combine them with the most recent methods used for bounding the number of D(1)-quintuples.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA