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Pregled bibliografske jedinice broj: 902384

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


Dujella, Andrej; Adžaga, Nikola; Kreso, Dijana; Tadić, Petra
Triples which are D(n)-sets for several n's // Analytic Number Theory and Related Areas / Fujita, Yasutsugu ; Misho, Hidehiko (ur.).
Kyoto: Research Institute for Mathematical Sciences, 2017. str. 6-6 (pozvano predavanje, podatak o recenziji nije dostupan, sažetak, znanstveni)


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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.-1.11.2017

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



POVEZANOST RADA


Projekti:
HRZZ-IP-2013-11-6422 - Diofantove m-torke, eliptičke krivulje, Thueove i indeksne jednadžbe (DIOPHANTINE) (Dujella, Andrej, HRZZ - 2013-11) ( POIROT)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Građevinski fakultet, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb,
Fakultet ekonomije i turizma "Dr. Mijo Mirković", Pula

Profili:

Avatar Url Andrej Dujella (autor)

Avatar Url Nikola Adžaga (autor)

Avatar Url Petra Rihter Tadić (autor)

Poveznice na cjeloviti tekst rada:

docs.google.com sites.google.com

Citiraj ovu publikaciju:

Dujella, Andrej; Adžaga, Nikola; Kreso, Dijana; Tadić, Petra
Triples which are D(n)-sets for several n's // Analytic Number Theory and Related Areas / Fujita, Yasutsugu ; Misho, Hidehiko (ur.).
Kyoto: Research Institute for Mathematical Sciences, 2017. str. 6-6 (pozvano predavanje, podatak o recenziji nije dostupan, sažetak, znanstveni)
Dujella, A., Adžaga, N., Kreso, D. & Tadić, P. (2017) Triples which are D(n)-sets for several n's. U: Fujita, Y. & Misho, H. (ur.)Analytic Number Theory and Related Areas.
@article{article, author = {Dujella, Andrej and Ad\v{z}aga, Nikola and Kreso, Dijana and Tadi\'{c}, Petra}, year = {2017}, pages = {6-6}, keywords = {Diophantine triples}, title = {Triples which are D(n)-sets for several n's}, keyword = {Diophantine triples}, publisher = {Research Institute for Mathematical Sciences}, publisherplace = {Kyoto, Japan} }
@article{article, author = {Dujella, Andrej and Ad\v{z}aga, Nikola and Kreso, Dijana and Tadi\'{c}, Petra}, year = {2017}, pages = {6-6}, keywords = {Diophantine triples}, title = {Triples which are D(n)-sets for several n's}, keyword = {Diophantine triples}, publisher = {Research Institute for Mathematical Sciences}, publisherplace = {Kyoto, Japan} }




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