Naslov
Triples which are D(n)-sets for several n's

Autori
Dujella, Andrej ; Adžaga, Nikola ; Kreso, Dijana ; Tadić, Petra

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

Izvornik
Analytic Number Theory and Related Areas / Fujita, Yasutsugu ; Misho, Hidehiko - Kyoto : Research Institute for Mathematical Sciences, 2017, 6-6

Skup
Analytic Number Theory and Related Areas

Mjesto i datum
Kyoto, Japan, 30.10.2017. - 01.11.2017

Vrsta sudjelovanja
Pozvano predavanje

Vrsta recenzije
Podatak o recenziji nije dostupan

Ključne riječi
Diophantine triples

Sažetak
For a nonzero integer n, a set of distinct nonzero integers {; ; ; a_1, a_2, ... , a_m}; ; ; such that a_ia_j + 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. Such sets were first studied by Diophantus of Alexandria, and since then by many authors. We will briefly mention some recent results concering Diophantine m-tuples in integers, rationals and finite fields. 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, {; ; ; 8, 21, 55}; ; ; is a D(1) and D(4321)-triple, while {; ; ; 1, 8, 120}; ; ; is a D(1) and D(721)-triple. We will present several infinite families of Diophantine triples {; ; ; a, b, c}; ; ; which are also D(n)-sets for two distinct $n$'s with n <> 1, as well as some Diophantine triples which are also D(n)-sets for three distinct n's with n <> 1. We will also discuss some related questions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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