Zagreb Üniversitesi (Hırvatistan) Matematik Bölümü öğretim elemanı Prof. Dr. Andrej Dujella 29.11.2019 Cuma Günü Saat 14.00’ da Bölüm katındaki MAT111 No'lu Lisansüstü Dersliğinde “ Triples and quadruples which are D(n)-sets for several n's” adlı bir konuşma yapmıştır. 

Katılım gösterenlere teşekkür ederiz.

Özet: For a nonzero integer n, a set of distinct nonzero integers {a1, a2, ... , am} such that ai aj + n is a perfect square for all 1 <= i < j <= m, is called a Diophantine m-tuple with the property D(n) or simply a D(n)-set. D(1)-sets are known as Diophantine m-tuples. It is natural to ask if there exists a Diophantine m-tuple (i.e. D(1)-set) which is also a D(n)-set for some n <> 1. For example, {1, 8, 120} is a D(1) and D(721)-triple. We will present infinite families of Diophantine triples {a, b, c} which are also D(n)-sets for two distinct n's with n <> 1, as  ell as some Diophantine triples which are also D(n)-sets for three distinct n's with n <> 1. We will consider similar problem with quadruples and we will show that there are infinitely many essentially different quadruples which are simultaneously D(n1)-quadruples and  (n2)-quadruples with n1 <> n2.